Question

Solve the equation. \(\left|x+\frac{3}{4}\right|=\frac{9}{4}\)

Short answer

The solutions to the equation are \(x=1.5\) and \(x=-3\).

Step-by-step solution

Formulate two equations from the given absolute value equation.

Rewrite the absolute value equation as two distinct equations. One positive and one negative, as \(x+\frac{3}{4}=\frac{9}{4}\) and \(x+\frac{3}{4}=-\frac{9}{4}\).

Solve the first equation

To solve \(x+\frac{3}{4}=\frac{9}{4}\), subtract \(\frac{3}{4}\) from both sides of the equation. This will give \(x=\frac{9}{4}-\frac{3}{4}\), simplifying to \(x=\frac{6}{4}\) or \(x=1.5\).

Solve the second equation

Similarly, to solve \(x+\frac{3}{4}=-\frac{9}{4}\), subtract \( \frac{3}{4}\) from both sides of the equation. Now you will get \(x=-\frac{9}{4}-\frac{3}{4}\), simplifying to \(x=-\frac{12}{4}\) or \(x=-3\).