How do you solve  3/4x + 11 = 20?

Feb 13, 2016

$x = 12$

Explanation:

First, get all the numbers to one side and the variable, x, to the other by subtracting 11 from both sides.

$\frac{3}{4} x + 11 = 20$
$\frac{3}{4} x = 9$

Multiple both sides of the reciprocal of the coefficient (the number in front of the variable) to get x. The reciprocal for a fraction can be obtained by flipping the denominator and the numerator. For example, the reciprocal of the fraction $\frac{2}{5}$ is $\frac{5}{2}$.

In this case, the coefficient is $\frac{3}{4}$, so its reciprocal would be $\frac{4}{3}$. Multiple both sides by $\frac{4}{3}$ to cancel out the coefficient and find the value of x.

$\left(\frac{4}{3}\right) \left(\frac{3}{4}\right) x = 9 \left(\frac{4}{3}\right)$

$x = 12$

Feb 14, 2016

$x = 12$

Explanation:

$\frac{3}{4} x + 11 = 20$

Subtract both sides by $11$:

$\frac{3}{4} x = 20 - 11$

$\frac{3}{4} x = 9$

Divide both sides by $\frac{3}{4}$

$x = 9 \div \frac{3}{4}$

$x = 9 \cdot \frac{4}{3}$

$x = \cancel{9} \cdot \frac{4}{\cancel{3}}$

$x = 3 \cdot 4 = 12$