Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE
description
Transcript of Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE
![Page 1: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/1.jpg)
NEXT
Click the ‘NEXT’ button to continue
![Page 2: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/2.jpg)
Today, in Ms. Stechschulte’s 7th grade class, we will be learning how to solve one-step equations. To navigate through this presentation, click on the arrows and buttons at the bottom of the screen. The arrow labeled ‘NEXT’, will take you to the next slide. The arrow labeled ‘BACK’, will take you back to the previous slide. When you get to the Main Menu, click on the first link to begin the lesson. If you need to go back to the previous lessons to clarify concepts, please do so.
Click the arrow below to continue.NEXT
![Page 3: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/3.jpg)
Your goal is to learn the concept of solving equations so you are successful answering the quiz questions. You must know the concepts well enough to solve two-step equations for tomorrow’s class. When you are finished with the first 2 Lessons, go to Lesson 3 and play the online math games for the remainder of the class period.
Good luck and have fun NEXTBACK
![Page 4: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/4.jpg)
“An equation is a written statement indicating the equality of two expressions”
It consists of a sequence of symbols that are split into left and right sides joined by an equal sign.
For example, 2 + 4 = 6 is an equation.
http://dictionary.reference.com/browse/equation
NEXT
Left side Right side
BACK
![Page 5: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/5.jpg)
* Remember *
2x + 3 = 5
NEXT
Coefficient: the number that is in front of the x. This means that 2 and x are multiplied.
Variable: the letter you are solving for; it needs to be isolated on one side of the equation. A variable can be any letter.
Left side Right side
BACK
![Page 6: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/6.jpg)
Lesson 1: Using adding & subtracting
Lesson 2: Using multiplication & division
Lesson 3: Online Math Games
Click on the link for Lesson 1 to begin.When finished with Lesson 1, continue with Lesson 2
then 3.
![Page 7: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/7.jpg)
Hoop Shoot
Equation Buster
Easy Algebra Equations
Say the ‘2 – steps’: Rags to Riches
BACK
![Page 8: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/8.jpg)
1x
=
111
x + 1 = 3To solve an equation you must get x
by itself on one side of the equal sign, while keeping the scale balanced
NEXTBACK
![Page 9: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/9.jpg)
=
x
1
111
NEXT
To get x by itself you have to take away (subtract) 1. However, this will cause the scale to become
unbalanced, so you also have to take away 1 from the other side of the equal sign.
BACK
![Page 10: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/10.jpg)
1
x
=
11
1
x + 1 = 3 -1 -1 x = 2
NEXT
After you subtract 1 from both sides of the equal sign, you are left with x = 2
BACK
![Page 11: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/11.jpg)
NEXT
“Two operations are said to be inverse to each other if one operation undoes the effect of the other operation.”
Addition and Subtraction are inverse operations
Multiplication and Division are inverse operations
http://www.icoachmath.com/Sitemap/InverseOperation.html BACK
![Page 12: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/12.jpg)
NEXT
Inverse operations must be used when solving equations.
In the previous example we SUBTRACTED to undo the ADDITION to get x by itself.
To solve x – 5 = 3,
what operation must you use to get x by itself?
BACK
![Page 13: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/13.jpg)
MORE EXAMPLES
If you said ADDITION you are correct! To undo SUBTRACTION you must ADD.
To solve
x – 5 = 3 +5 +5 x = 8
Add 5 to both sides to keep the equation balanced.
Begin Quiz
1BACK
![Page 14: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/14.jpg)
1x
=
111
x + 2 = 4To solve an equation get rid of whatever is with the
variable (x). What you do to one side, you must also do to the other side.
NEXT
11
![Page 15: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/15.jpg)
1
x
=
11
1
x + 2 = 4Subtract 2 from both sides to keep the scale
balanced
1 1
x = 2
To Quiz 1
NEXTBACK
![Page 16: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/16.jpg)
Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve
x – 2 = 3 +2 +2 x = 5
Add 2 to both sides to keep the equation balanced.
To Quiz 1 NEXTBACK
![Page 17: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/17.jpg)
-1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve
-1 = 7 + x -7 -7
-8 = xx = -8
Subtract 7 from both sides to keep the equation balanced.
To Quiz 1BACK
![Page 18: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/18.jpg)
Question 1:
Solve x + 4 = 9
A. x = 13B. x = 5C. x = 9
Click on a letter to continue.
![Page 19: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/19.jpg)
Question 2:
Solve x – 5 = 2
A. x = -3B. x = 2C. x = 7
Click on a letter to continue.
![Page 20: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/20.jpg)
Question 3:
Solve – 5 = 4 + x
A. x = -9B. x = -1C. x = 9
Click on a letter to continue.
![Page 21: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/21.jpg)
Correct!!
Nice Work! NEXT
![Page 22: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/22.jpg)
Correct!!
Great Job! NEXT
![Page 23: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/23.jpg)
Correct!!
Fabulous! NEXT
![Page 24: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/24.jpg)
IncorrectTry Again
Let’s look at another example NEXT
![Page 25: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/25.jpg)
1x
=
111
x + 2 = 4To solve an equation get rid of whatever is with the
variable (x). What you do to one side, you must also do to the other side.
NEXT
11
![Page 26: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/26.jpg)
1
x
=
11
1
x + 2 = 4Subtract 2 from both sides to keep the scale
balanced
1 1
x = 2
To Quiz 1
BACK
![Page 27: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/27.jpg)
IncorrectTry Again
Let’s look at another example NEXT
![Page 28: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/28.jpg)
Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve
x – 2 = 3 +2 +2 x = 5
Add 2 to both sides to keep the equation balanced.
To Quiz 1
![Page 29: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/29.jpg)
IncorrectTry Again
Let’s look at another example NEXT
![Page 30: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/30.jpg)
-1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve
-1 = 7 + x -7 -7
-8 = xx = -8
Subtract 7 from both sides to keep the equation balanced.
To Quiz 1
![Page 31: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/31.jpg)
What is the inverse operation of
MULTIPLICATION?
NEXTBACK
![Page 32: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/32.jpg)
The answer is…
DIVISION
NEXTBACK
![Page 33: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/33.jpg)
What is the inverse operation of DIVISION?
NEXTBACK
![Page 34: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/34.jpg)
The answer is…
MULTIPLICATION
NEXTBACK
![Page 35: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/35.jpg)
When you have an equation with
multiplication or division, you will do the
inverse operation to solve!
NEXTBACK
![Page 36: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/36.jpg)
Since 6 and x are multiplied, to solve, we divide by 6.
6x = 48 6x = 48
6 6x = 8
Divide by 6 on both sides to keep the equation balanced.
BACK NEXTReminder: When a number is divided by itself, it equals 1.
![Page 37: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/37.jpg)
Since x is divided by 4, to solve, we multiply by 4.
x = 5 4
(4)x = 5(4) 4
x = 20
Multiply by 4 on both sides to keep the equation balanced.
To Quiz 2BACK
MORE EXAMPLES
![Page 38: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/38.jpg)
The inverse operation of MULTIPLICATION is DIVISION, so we
divide by 10.
10x = 30 10x = 30
10 10x = 3
Divide by 10 on both sides to keep the equation balanced.
NEXTTo
Quiz 2BACK
![Page 39: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/39.jpg)
The inverse operation of DIVISION is MULTIPLICATION, so we multiply by -5.
x = 3 -5
(-5)x = 3(-5) -5
x = -15
Multiply by -5 on both sides to keep the equation balanced.
NEXT
To Quiz 2
** Remember: Negative times a positive = negative
BACK
![Page 40: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/40.jpg)
The inverse operation of MULTIPLICATION is DIVISION, so we
divide by -2.
-2x = -10 -2x = -10
-2 -2x = 5
Divide by -2 on both sides to keep the equation balanced.
To Quiz 2
** Remember: Negative times a negative = positive
BACK
![Page 41: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/41.jpg)
Question 1:
Solve 5x = 35
A. x = 175B. x = 30C. x = 7
Click on a letter to continue.
![Page 42: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/42.jpg)
IncorrectTry Again
Let’s look at another example NEXT
![Page 43: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/43.jpg)
Correct!!
Super! NEXT
![Page 44: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/44.jpg)
Question 2:
Solve x = 4
-2A. x = -8B. x = 6C. x = -2
Click on a letter to continue.
![Page 45: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/45.jpg)
IncorrectTry Again
Let’s look at another example NEXT
![Page 46: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/46.jpg)
Correct!!
Fantastic! NEXT
![Page 47: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/47.jpg)
Question 3:
Solve -3x = 6
A. x = 2B. x = -2C. x = -18
Click on a letter to continue.
![Page 48: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/48.jpg)
IncorrectTry Again
Let’s look at another example NEXT
![Page 49: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/49.jpg)
Correct!!
Great Job! NEXT
![Page 50: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/50.jpg)
The inverse operation of MULTIPLICATION is DIVISION, so we
divide by 10.
10x = 30 10x = 30
10 10x = 3
Divide by 10 on both sides to keep the equation balanced.
To Quiz 2
![Page 51: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/51.jpg)
The inverse operation of DIVISION is MULTIPLICATION, so we multiply by -5.
x = 3 -5
(-5)x = 3(-5) -5
x = -15
Multiply by -5 on both sides to keep the equation balanced.
To Quiz 2
** Remember: Negative times a positive = negative
![Page 52: Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE](https://reader035.fdocuments.us/reader035/viewer/2022070406/56814116550346895dacdca4/html5/thumbnails/52.jpg)
The inverse operation of MULTIPLICATION is DIVISION, so we
divide by -2.
-2x = -10 -2x = -10
-2 -2x = 5
Divide by -2 on both sides to keep the equation balanced.
To Quiz 2
** Remember: Negative times a negative = positive