Warmups
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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
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
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
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.