# How do you solve abs(2x+3)+4=5x?

Aug 5, 2017

$x = \frac{1}{7} , \frac{7}{3}$

Refer to the explanation for the process.

#### Explanation:

Solve:

$\left\mid 2 x + 3 \right\mid + 4 = 5 x$

Since $\left\mid a \right\mid = a$ and $\left\mid - a \right\mid = a$, there is both a positive and negative component to the equation, therefore you will have two equations to solve.

First Equation: (2x+3) is Positive

$2 x + 3 + 4 = 5 x$

Subtract $2 x$ from both sides.

$3 + 4 = 5 x - 2 x$

Simplify.

$7 = 3 x$

Divide both sides by $3$.

$\frac{7}{3} = x$

Switch sides.

$x = \frac{7}{3}$

Second Equation: (2+3) is Negative

$- \left(2 x + 3\right) + 4 = 5 x$

Simplify.

$- 2 x - 3 + 4 = 5 x$

Add $2 x$ to both sides.

$- 3 + 4 = 5 x + 2 x$

Simplify.

$1 = 7 x$

Divide both sides by $7$.

$\frac{1}{7} = x$

Switch sides.

$x = \frac{1}{7}$

Therefore:

$x = \frac{1}{7} , \frac{7}{3}$