Must show ALL steps and ALL work for credit Equations - Introduction.
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Transcript of Must show ALL steps and ALL work for credit Equations - Introduction.
![Page 1: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/1.jpg)
Must show ALL steps and ALL work for credit
Equations - Introduction
![Page 2: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/2.jpg)
VocabularyVocabulary
Equation Equation
Solution Solution
Inverse OperationInverse Operation
Insert Lesson Title Here
Course 2
1-10 Equations and Their Solutions
![Page 3: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/3.jpg)
Ella has 22 CDs. This is 9 more than her friend Kay has.
This situation can be written as an equation.An equation is a mathematical statement that two expressions are equal in value.
An equation is like a balanced scale.
Right expressionLeft expression
Number of CDs Ella has
22
is equalto=
9 more thanKay hasj + 9
Course 2
1-10 Equations and Their Solutions
![Page 4: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/4.jpg)
Just as the weights on both sides of a balanced scale are exactly the same, the expressions on both sides of an equation represent exactly the same value.
When an equation contains a variable, a value of the variable that makes the statement true is called a solution of the equation.
22 = j + 9 j = 13 is a solution because 22 = 13 + 9.
22 = j + 9 j = 15 is not a solution because 22 15 + 9.
The symbol ≠ means “is not equal to.” Reading Math
Course 2
1-10 Equations and Their Solutions
![Page 5: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/5.jpg)
Determine whether the given value of the variable is a solution of t + 9 = 17.
Additional Example 1A: Determining Whether a Number is a Solution of an Equation
26
26 + 9 = 17?
35 = 17?
26 is not a solution of t + 9 = 17.
Substitute 26 for t.
t + 9 = 17
Course 2
1-10 Equations and Their Solutions
![Page 6: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/6.jpg)
Additional Example 1B: Determining Whether a Number is a Solution of an Equation
Determine whether the given value of the variable is a solution of t + 9 = 17.
8
8 + 9 = 17?
17 = 17?
8 is a solution of t + 9 = 17.
Substitute 8 for t.
t + 9 = 17
Course 2
1-10 Equations and Their Solutions
![Page 7: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/7.jpg)
LearnLearn to solve one-step equations. to solve one-step equations.
Sections 1.11 and 1.12 in textbook.Sections 1.11 and 1.12 in textbook.
Course 2
12-1 Solving Two-Step Equations
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How to solve one-step equations
1. Goal – Get the variable alone2. Use the inverse operation to undo
On BOTH sides of the equationAddition and Subtraction are inverse operationsMultiplication and Division are inverse
operations**Remember – Whatever you do to one side you MUST do
to the other side!!!
![Page 9: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/9.jpg)
2-Column NotesExample #1b + 2 = 6 Step 1
-2 -2 Step 2
b = 4 Step 3
Check 4 + 2 = 6 Step 4
6 = 6 Step 5
Instructions – STEPS
1) Copy Problem2) Inverse Operation
on BOTH sides*Do the Math!!!!
3) Solution – Box –in4) Check AnswerRewrite equation with Value substituted5) Do Math and check
BOTH sides
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2-Column NotesExample #2n – 36 = 17 Step 1
+36 +36 Step 2
n = 53 Step 3
Check 53–36 = 17 Step 4
17 = 17 Step 5
Instructions – STEPS
1) Copy Problem2) Inverse Operation
on BOTH sides*Do the Math!!!!
3) Solution – Box –in4) Check AnswerRewrite equation with Value substituted5) Do Math and check
BOTH sides
![Page 11: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/11.jpg)
2-Column NotesExample #318 + j =94 Step 1
-18 -18 Step 2
j = 76 Step 3
Check 18+76=94 Step
4
94 = 94 Step 5
Instructions – STEPS
1) Copy Problem2) Inverse Operation
on BOTH sides*Do the Math!!!!
3) Solution – Box –in4) Check AnswerRewrite equation with Value substituted5) Do Math and check
BOTH sides
![Page 12: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/12.jpg)
2-Column NotesExample #4
Step 1 Step 2
Step 3 Step 4
Step 5
Instructions – STEPS
1) Copy Problem2) Inverse Operation
on BOTH sides*Do the Math!!!!
3) Solution – Box –in4) Check AnswerRewrite equation with Value substituted5) Do Math and check
BOTH sides
9 108
9 108
9 912
9 12 108
108 108
q
q
q
check
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2-Column NotesExample #5
Step 1 Step 2 Step 3 Step 4
Step 5
Instructions – STEPS
1) Copy Problem2) Inverse Operation
on BOTH sides*Do the Math!!!!
3) Solution – Box –in4) Check AnswerRewrite equation with Value substituted5) Do Math and check
BOTH sides
135
5 13 55
65
6513
513 13
z
z
z
check
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2-Column NotesExample #6
Step 1 Step 2
Step 3 Step 4
Step 5
Instructions – STEPS
1) Copy Problem2) Inverse Operation
on BOTH sides*Do the Math!!!!
3) Solution – Box –in4) Check AnswerRewrite equation with Value substituted5) Do Math and check
BOTH sides
2211
11 22 1111242
24222
1122 22
w
w
w
check
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When you solve equations that have one operation, you use an inverse operation toisolate the variable. You can also use inverseoperations to solve equations that have morethan one operation.
n + 7 = 15– 7 –7
n = 8
2x + 3 = 23
– 3 – 32x = 20 You need to use
another operationto isolate x.
It is often a good plan to follow the order of operations in reverse when solving equationsthat have more than one operation.
Course 2
12-1 Solving Two-Step Equations
![Page 16: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/16.jpg)
LearnLearn to solve two-step equations. to solve two-step equations.
Course 2
12-1 Solving Two-Step Equations
![Page 17: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/17.jpg)
Write down the directions to get to Pope High School from Hightower Trail MS parking lot.Directions to the
HSExplain how to
return to Hightower Trail MS.
![Page 18: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/18.jpg)
Can you think of any other situations where you have to work backwards??????
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How can the order of operations help us solve equations????List the order of
operations1.
2.
3.
4.
Now list it going backwards
1.
2.
3.
4.
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Solve. Check each answer.
Additional Example 1A: Solving Two-Step Equations Using Division
9c + 3 = 39
9c + 3 = 39
– 3 –39c = 36
c = 4
Subtract 3 from both sides.
Divide both sides by 9.9c9
= 36 9
Course 2
12-1 Solving Two-Step Equations
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Check.
Additional Example 1A Continued
9c + 3 = 39
9(4) + 3 39?=
?=
?=
36 + 3 39
39 39
Substitute 4 for c.
4 is a solution.
Course 2
12-1 Solving Two-Step Equations
![Page 22: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/22.jpg)
Course 2
12-1 Solving Two-Step Equations
Reverse the order of operations when solving equations that have more than one operation.
Helpful Hint
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Solve. Check the answer.
7c + 6 = 48
7c + 6 = 48
– 6 –67c = 42
c = 6
Subtract 6 from both sides.
Divide both sides by 7.7c7
= 42 7
Check It Out: Example 1A
Course 2
12-1 Solving Two-Step Equations
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Check It Out: Example 1A Continued
Insert Lesson Title Here
Check.
7c + 6 = 48
7(6) + 6 48?=
?=
?=
42 + 6 48
48 48
Substitute 6 for c.
6 is a solution.
Course 2
12-1 Solving Two-Step Equations
![Page 25: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/25.jpg)
Solve.
Additional Example 2A: Solving Two-Step Equations Using Multiplication
6 + y5 = 21y5 = 216 +
– 6 –6y5
= 15
y5
= (5)15(5)
y = 75
Subtract 6 from both sides.
Multiply both sides by 5.
Course 2
12-1 Solving Two-Step Equations
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Solve.
Additional Example 2B: Solving Two-Step Equations Using Multiplication
x7 – 11 = 9
x7 – 11 = 9
x7 = 20
x7 = (7)20(7)
x = 140
Add 11 to both sides.
Multiply both sides by 7.
+11 +11
Course 2
12-1 Solving Two-Step Equations
![Page 27: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/27.jpg)
Check It Out: Example 2A
Insert Lesson Title Here
Solve.
8 + y2 = 48y2 = 488 +
– 8 –8y2 = 40
y2
= (2)40(2)
y = 80
Subtract 8 from both sides.
Multiply both sides by 2.
Course 2
12-1 Solving Two-Step Equations
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Check It Out: Example 2B
Insert Lesson Title Here
Solve.
x5 – 31 = 19
x5 – 31 = 19
+31 +31x5 = 50
x5 = (5)50(5)
x = 250
Add 31 to both sides.
Multiply both sides by 5.
Course 2
12-1 Solving Two-Step Equations
![Page 29: Must show ALL steps and ALL work for credit Equations - Introduction.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f275503460f94c3eb1f/html5/thumbnails/29.jpg)
Out ticket Show each step and number each stepSolve and Check
1. 4w – 3 = 25 2.
2 123
x