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How would you solve this equation? (100)-(90+x)=-30

3 Answers

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By simplifying, combining like terms, then rearranging to isolate x.

Here's the important first step. Remember that when you subtract an expression in parentheses, that multiplies everything inside the parentheses by -1, changing the sign.

Example: 5 - (4 - x) = 5 + (-1)(4 - x) = 5 + (-4) + x = 1 + x

Example: 5 - (2 + x) = 5 + (-1)(2 + x) = 5 + (-2) + (-x) = 3 - x

Do that with your left hand side.
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If you multiply the second set of parentheses by -1, so +90 -x, then you just do algebra like normal.  So 100 + 90 - x= -30. 190 - x =-30. -x= -220. -220/-1= 220.
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If distributive property is trouble for you, add (90 + x) to both sides.

(100) - (90 + x) + (90 + x) = -30 + (90 + x)

Simplify left side since 100 - b + b means 100.

100 = -30 + 90 + x

Simplify right side by adding -30 and 90.

100 = 60 + x

Now subtract 60 from both sides.

100 - 60 = 60 + x - 60

40 = x

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