Chapter 7 Lesson 1 Solving Equations with Variables on Each Side pgs. 330-333 What you will learn:...
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Transcript of Chapter 7 Lesson 1 Solving Equations with Variables on Each Side pgs. 330-333 What you will learn:...
Chapter 7 Lesson 1Solving Equations with Variables on
Each Sidepgs. 330-333
Chapter 7 Lesson 1Solving Equations with Variables on
Each Sidepgs. 330-333
What you will learn:Solve equations with variables on
each side
What you will learn:Solve equations with variables on
each side
To solve equations with variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variables on
one side. Then solve the equation.
To solve equations with variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variables on
one side. Then solve the equation.
Quick Review: Chapter 3-3 (pg. 110-111)Subtraction Property of Equality: If you subtract the same number
from each side of an equation, the two sides remain equal. Ex.) x + 2 = 3
x + 2 – 2 = 3 – 2x = 1
Addition Property of Equality: If you add the same number to each side of an equation, the two sides remain equal.
Ex.) x – 2 = 5 x – 2 + 2 = 5 + 2 x = 7
Quick Review: Chapter 3-3 (pg. 110-111)Subtraction Property of Equality: If you subtract the same number
from each side of an equation, the two sides remain equal. Ex.) x + 2 = 3
x + 2 – 2 = 3 – 2x = 1
Addition Property of Equality: If you add the same number to each side of an equation, the two sides remain equal.
Ex.) x – 2 = 5 x – 2 + 2 = 5 + 2 x = 7
Example 1: Equations with Variables on Each Side
Example 1: Equations with Variables on Each Side
Remember, the goal is to isolate the variable by itself!
Solve 4x – 8 = 5x Step 1: Rewrite the problem 4x – 8 = 5xStep 2: Subtract 4x from each side to isolate the variable 4x – 8 = 5x Remember, what you do -4x = -4x one side of the equation, - 8 = x you must also do to the
other side!!!
Remember, the goal is to isolate the variable by itself!
Solve 4x – 8 = 5x Step 1: Rewrite the problem 4x – 8 = 5xStep 2: Subtract 4x from each side to isolate the variable 4x – 8 = 5x Remember, what you do -4x = -4x one side of the equation, - 8 = x you must also do to the
other side!!!
Now check: Substitute -8 everywhere there is an x. 4(-8) – 8 = 5(-8)
-32 – 8 = -40 -32 + (-8) = -40 -40 = -40
Example 2: Equations with Variables on Each Side
Example 2: Equations with Variables on Each Side
Solve 4k + 24 = 6k - 10
First, choose the side to isolate the variable on, hint: when isolating the variable, try to keep it positive.
Solve 4k + 24 = 6k - 10
First, choose the side to isolate the variable on, hint: when isolating the variable, try to keep it positive.
4k + 24 = 6k – 104k + 24 = 6k – 10
4k + 24 = 6k – 10 - 4k -4k Start by subtracting 4k from each
side
24 = 2k – 10 New equation (look familiar?)
+10 + 10 Add 10 to both sides
34 = 2k New equation (look familiar?)
2 2 17 = k Solve
4k + 24 = 6k – 10 - 4k -4k Start by subtracting 4k from each
side
24 = 2k – 10 New equation (look familiar?)
+10 + 10 Add 10 to both sides
34 = 2k New equation (look familiar?)
2 2 17 = k Solve
Now check: 4(17) + 24 = 6(17) – 10 68 + 24 = 102 – 10 92 = 92
Solve: 3.1w + 5 = 0.8 + wSolve: 3.1w + 5 = 0.8 + w
3.1w + 5 = 0.8 + w
- 1.0w - w 2.1w + 5 = 0.8 - 5 - 5.0 2.1w = -4.2 2.1 2.1 w = -2
3.1w + 5 = 0.8 + w
- 1.0w - w 2.1w + 5 = 0.8 - 5 - 5.0 2.1w = -4.2 2.1 2.1 w = -2
Check:3.1(-2) + 5 = 0.8 + (-2)-6.2 + 5 = -1.2 -1.2 = -1.2
Example 3: Use an Equation to Solve a Problem
Example 3: Use an Equation to Solve a Problem
Define a variable and write an equation to find each number. Then solve.
One cell phone carrier charges $29.75 a month plus $0.15 a minute for local calls. Another carrier charges $19.95 a month and $0.29 a minute for local calls. For how many minutes is the cost of the plans the same?
Let m represent the number of minutes.
Define a variable and write an equation to find each number. Then solve.
One cell phone carrier charges $29.75 a month plus $0.15 a minute for local calls. Another carrier charges $19.95 a month and $0.29 a minute for local calls. For how many minutes is the cost of the plans the same?
Let m represent the number of minutes.
Words: $29.75 + $0.15 for each minute $19.95 + $0.29 for each minuteVariables: 29.75 + .15m 19.95 + .29mEquation: 29.75 + .15m = 19.95 + .29m
Solve: 29.75 + .15m = 19.95 +.29m - .15m -.15m 29.75 = 19.95 + .14m -19.95 = -19.95 9.8 = .14m 70 = m
So, the cost of the plansIs the same for the first 70 minutes
Your turn!Your turn!A. 4x + 9 = 7x
B. -s + 4 = 7s – 3
C. 12.4y + 14 = 6y – 2
D. Twice a number is 220 less than six times the number. What is the number?
A. 4x + 9 = 7x
B. -s + 4 = 7s – 3
C. 12.4y + 14 = 6y – 2
D. Twice a number is 220 less than six times the number. What is the number?
4x + 9 = 7x Check:-4x = -4x 4(3) + 9 = 7(3) 9 = 3x 12 + 9 = 21 3 = x 21 = 21
-s + 4 = 7s – 3 Check:+s +s -.875 + 4 = 7(.875) - 3 4 = 8s – 3 3.125 = 6.125 - 3 +3 + 3 3.125 = 3.125 7 = 8s .875 = s
Y = -2.5 Check: 12.4(-2.5) + 14 = 6(-2.5) – 2 -31 + 14 = -15 – 2 -17 = -17
2n = 6n – 220 Check: 2(55) = 6(55) – 220 n = 55 110 = 330 – 220 110 = 110
Extra Practice by the door on your way out!!
Extra Practice by the door on your way out!!