7(a+3)=(-119)

Question

How would you solve this equation

Answer 1

Hi, Wayne.

The first step to solve this equation is to get rid of the parentheses. On the left, we use the distributive property to multiply the 7 by both terms inside the parentheses: (the asterisk stands for multiplication)

7 * a + 7 * 3 = (-119)

7a + 21 = (-119)

On the right, there is no operation to do, so we can just drop the parentheses:

7a + 21 = -119

Now we "undo" what is done to the variable, to get the variable all by itself.  To "undo" the + 21, we subtract 21. We have to do the same thing to both sides of the equation to keep it in balance. So:

7a + 21 - 21 = -119 - 21

The + 21 - 21 cancel out on the left; on the right we have a -119 and -21, so we get:

7a = - 140

The 7a means "7 times a" (since it is a letter and a number, we don't need a multiplication sign). To undo multiplication, we divide by 7, and we do it to both sides. (I am using the / to indicate division.)

7a / 7 = -140 / 7

7 divided by 7 is 1, so we have 1a on the left. 1a can also be written as plain a. On the right, -140 divided by 7 is -20, so:

a = -20

There is our answer. We can check it by plugging it back into the original equation:

7(-20 + 3) = (-119)

7(-17) = (-119)

7 times -17 is indeed -119, so our answer is correct.

 

Hope this helps!

Kathye