2. Chapter 7 Lesson 1 Solving Equations with Variables on Each Side pgs. 330-333 What you will learn: Solve equations with variables on each side What you will learn: Solve equations with variables on each side

3. 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 – 2 x = 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 – 2 x = 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

4. 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 = 5x Step 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 = 5x Step 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 

5. 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.

6. 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 

7. Solve: 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 

8. 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 minute Variables: 29.75 +.15m 19.95 +.29m Equation: 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 plans Is the same for the first 70 minutes

9. 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 

10. Extra Practice by the door on your way out!!