How do you solve -7( a + 6) + 2= 8- 3( 6a + 5)?

1 Answer
Sep 22, 2017

a=3

Explanation:

First, we will look at the left side of the equation, which is -7(a+6)+2.
We will leave the +2 aside for now.
We will distribute parentheses/brackets using: x(y+z)=xy+xz

In this case, x would represent -7, y will represent a and z represents 6.

This means that -7(a+6) is equal to -7*a+ -7*6.
+ - is the same as - so the equation would be -7*a-7*6.

7*6=42
The whole equation now (including the +2) would be 7a-42+2.

-42+2=-40 so the equation now would be -7a-40.

Let's take a look on the right side now which is 8-3(6a+5).
We will leave the 8 aside for now.
We will distribute parentheses/brackets again using the same thing: x(y+z)=xy+xz.

In this case, x represents -3, y represents 6a and z represents 5. Don't forget that + - is equal to -!

Since x represents -3, y represents so and so, the equation will be -3*6acancel(+)-3*5

-3*6a=-18a and 3*5=15.
So, -3*6a-3*5 is the same as -18a-15.
Now, we will add in the 8.

Equation:
8-18a-15
We will group like terms:
-18a+8-15 and 8-15=-7.
The equation will now be -18a-7.

There you go! You simplified both sides. Now we can solve for a.
Whole equation:
-7a-40=-18a-7. Now we add 40 to both sides.
-7a-40color(blue)+color(blue)40=-18a-7color(blue)+color(blue)40 which is the same as -7a=-18a+33.

Now we add 18a to both sides.
-7acolor(blue)+color(blue)18color(blue)a=-18a+33color(blue)+color(blue)18color(blue)a.

Now we simplify it to be 11a=33. Divide both sides by 3 and you get a=3.