Four times the sum of twice a number and 5 is -12

Question

I don't know how to get the answer

 

Answer 1

The trick is trying to interpret what they're asking.

"4 times the sum" means that we need to multiply after adding, so we're going to need parentheses:

4()

"sum of twice the number and 5" means that we're going to multiply an unknown, and then add 5 to it:

4(2x + 5)

"is -12" means that's our final answer:

4(2x + 5) = -12

 

So now we need to isolate x. Start by dividing both sides by 4:

^{4(2x + 5)} / ₄ = -¹²/₄

2x + 5 = -3

Subtract 5:

2x + 5 - 5 = -3 - 5

2x = -8

Divide by 2:

^2x/₂ = -⁸/₂

x = -4

 

Check:

4(2 * -4 + 5) = -12

4(-8 + 5) = -12

4 * -3 = -12

-12 = -12