Dillard

2021-02-13

$\frac{3}{4}\left(4x-8\right)=-10$

pierretteA

To solve an equation, we need to isolate the variable term and then isolate the variable using inverse operations.
Before we can isolate the variable term, we need to simplify the left side of the equation.
The Distributive Property states that $a\left(b+c\right)=ab+ac$ so using the Distributive Property on the left side of the equation gives:
$\frac{3}{4}\left(4x-8\right)=-10$
$\frac{3}{4}\left(4x\right)-\frac{3}{4}\left(8\right)=-10$
$3x-6=-10$
Now that the left side is simplified, we can isolate the variable term of 3x. Since 6 is being subtracted from 3x, we need to add 6 on both sides because addition is the inverse operation of subtraction:
$3x-6+63x=-10+6$
$3x=-4$
We can no isolate the variable. Since the variable x is being multiplied by 3, we need to divide both sides by 3 because division is the inverse operation of multiplication:
$\frac{3x}{3}=-\frac{4}{3}$
$x=-\frac{4}{3}$
The solution of the equation is then $x=-\frac{4}{3}$

Do you have a similar question?