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.

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Presentation transcript:

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 x + 2 = x = -3 Check! 3(-3) + 2 = 2(-3) – = -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.

E XAMPLE 2 5x + 2 = 5 – x + x 6x + 2 = x = x = 1/2 Check! 5(1/2) + 2 = 5 – 1/ = 5 – = 4.5

TOO with a partner 1) 4x + 6 = 2x – 8 Answers: 1) x = -7 2) 7 – 3x = 10 – 4x 2) x = 3

S PECIAL C ASES 7 – 3x = x – 8 – 4x 7 – 3x = -8 – 3x + 3x + 3x 7 = -8 False! Answer: No Solution -6n + 15 = 15 – 6n + 6n 15 = 15 True! Answer: All Numbers

Distributive Property Example 1 3(x + 2) = 18 3x + 6 = x = x = 4 Check! 3(4 + 2) = 18 PEMDAS! 3(6) = = 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) = 10 2) 2x + 3(2 – x) = 10 3) 4 – 3(x + 7) = 30 Answers: 1) x = -9 2) x = -4 3) x = -47/3

EXAMPLE 4 2(x – 3) + 5 = 3(x – 1) 2x – = 3x – 3 2x – 1 = 3x – 3 - 2x -2x -1 = x – = x x = 2 Steps 1) Distribute 2) Combine Like Terms 3) Move Variables 4) Add/Subtract 5) Multiply/Divide Final Answer: x = #

T OO F OR H OMEWORK 1) 2 + 6x – 3 = 8x + 4 – 2x 2) -10x x = 6 – 4x – 1 3) 12x + 5 = x – 5 – 2x Two are special cases One is normal Steps Combine Like Terms Move Variables Add/Subtract Multiply/Divide

Homework Worksheet #23

M ATH L AB W ARMUPS 1. 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.

A GENDA Finish Bingo Homework Time