You have an equation with the variable x.
You want to know what value of x makes the equation true.
The first step is to simplify the left side by distributing on both sets of parentheses.
- (1 + 7x) - 6 (-7 - x) = 36
Distribute the negative sign. It changes every sign inside the parentheses.
Distribute the -6. Multiply each number inside the parentheses by -6.
-1 - 7x + 42 + 6x = 36
Now combine like terms on the left side.
-x + 41 = 36
Subtract 41 from both sides.
-x = -5
Divide both sides by -1.
x = 5
Our solution is x = 5.
We can now check to see if it is correct.
We replace x with 5 in the original equation and see it the statement is true.
- (1 + 7x) - 6 (-7 - x) = 36
- (1 + 7*5) - 6 (-7 - 5) = 36
- (1 + 35) - 6(-12) = 36
-36 - (-72) = 36
-36 + 72 = 36
36 = 36
Since 36 = 36 is a true statement, our solution, x = 5, is correct.