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7(a+3)=(-119)

How would you solve this equation

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