eight times the sum of 7 and some number is -24

Question

I am having trouble setting this up.

Answer 1

Hi Krum!
The difficult part of these questions is definitely setting up the equation! Any time you're solving for some number, set that as x. In this question, we need to find x such that 8 times the sum of x and 7 is -24. Because we're multiplying 8 to the sum of x+7, the sum has to be in parenthesis, because we need to solve that part before multiplying by 8:

8(7+x)=-24

 

Now we use the distributive property to get rid of the parenthesis on the left side:

(8*7)+(8*x)=-24

56+8x=-24       or       8x+56=-24

 

Next, subtract 56 from both sides of the equation

(8x+56)-56 = (-24)-56

8x=-80

 

And finally, divide both sides by 8:

(8x)÷8 = (-80)÷8

x=-10

 

With these types of problems, it's always best to check your answer by plugging x back into your original equation and making sure it works:

8(7+x)=-24

8(7+(-10))=-24

8(-3)=-24

-24=-24    as needed