Answer
x = 20
Work Step by Step
$\frac{3x}{4}$ - 3 = $\frac{x}{2}$ + 2
We can start by adding 3 to both sides of the equation, getting:
$\frac{3x}{4}$ - 3 + 3 = $\frac{x}{2}$ + 2 + 3
Performing the arithmetic, we get:
$\frac{3x}{4}$ = $\frac{x}{2}$ + 5
Subtract $\frac{x}{2}$ from both sides of the equation.
$\frac{3x}{4}$ - $\frac{x}{2}$ = $\frac{x}{2}$ - $\frac{x}{2}$ + 5
$\frac{3x}{4}$ - $\frac{x}{2}$ = 5
Now, rewrite each fraction using the common denominator of 4.
$\frac{3x}{4}$ - $\frac{2x}{4}$ = 5
Next, complete the operation of subtraction on the left side of the equation and write 5 as a fraction by writing it over a denominator of 1. :
$\frac{x}{4}$ = $\frac{5}{1}$
WE can then cross multiply and get x = 20.
To check our answer, we can substitute 20 back into the original equation for x.
$\frac{(3)(20)}{4}$ - 3 = $\frac{20}{2}$ + 2
Then complete the arithmetic getting: $\frac{60}{4}$ - 3 = $\frac{20}{2}$ + 2.
Continue with the arithmetic: 15 - 3 = 10 + 2
Last, add/subtract on each side of the equation.
12 = 12
Our answers match, so our solution of x = 20 is correct.
