Warmups

1. What is the supplement of 56°?

2. What is the complement of (3x)°?

3. Find three consecutive even integers whose sum is 54.

3-5 SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES

Objective: To solve equations with the variable on both sides, and to use the distributive property to solve equations.

EXAMPLE 1

3x + 2 = 2x – 1 -2x -2x x + 2 = -1 - 2 - 2 x = -3

Check!3(-3) + 2 = 2(-3) – 1-9 + 2 = -6 – 1-7 = -7

If variables are on different sides, you can NOT combine them!

Must add/subtract to the other side.

Always move the smaller coefficient.

Example 2

5x + 2 = 5 – x + x + x 6x + 2 = 5 - 2 - 2 6x = 3 6 6 x = 1/2

Check!5(1/2) + 2 = 5 – 1/22.5 + 2 = 5 – 0.54.5 = 4.5

3

3

TOO with a partner

1) 4x + 6 = 2x – 8

Answers:1) x = -7

2) 7 – 3x = 10 – 4x

2) x = 3

Special Cases

7 – 3x = x – 8 – 4x7 – 3x = -8 – 3x + 3x + 3x 7 = -8

False!Answer: No Solution

-6n + 15 = 15 – 6n+ 6n + 6n 15 = 15

True!Answer: All Numbers

Distributive Property Example 1

3(x + 2) = 18 3x + 6 = 18 - 6 - 6 3x = 12 3 3 x = 4

Check!3(4 + 2) = 18

PEMDAS!3(6) = 1818 = 18

Examples

2) 4(x – 3) = 24

Answers:2) x = 9

3) -2(5 + x) = 3

3) x = -13/2

TOO with a partner

1) 4 – (x + 3) = 102) 2x + 3(2 – x) = 103) 4 – 3(x + 7) = 30

Answers:1) x = -92) x = -43) x = -47/3

EXAMPLE 4

2(x – 3) + 5 = 3(x – 1) 2x – 6 + 5 = 3x – 3 2x – 1 = 3x – 3 - 2x -2x -1 = x – 3 +3 + 3 2 = x

x = 2

Steps1) Distribute2) Combine Like Terms3) Move Variables4) Add/Subtract5) Multiply/DivideFinal Answer: x = #

Too For Homework

1) 2 + 6x – 3 = 8x + 4 – 2x2) -10x + 5 + 2x = 6 – 4x – 13) 12x + 5 = 10 + 14x – 5 –

2x

Two are special casesOne is normal

Steps Combine Like Terms Move Variables Add/Subtract Multiply/Divide

Homework

Worksheet #23

Math Lab Warmups1. The sum of three consecutive integers is 54.

Find the three numbers.

2. The sum of 2 consecutive even integers is 114. Find the two numbers.

3. The sum of four consecutive even integers is 228. Find the four numbers.

Agenda

Finish Bingo Homework Time