Question

Solve the equation. $$|3 x+2|+2=5$$

Short answer

The solutions to the equation are \(x = -\frac{5}{3}\) and \(x = \frac{1}{3}\)

Step-by-step solution

Remove the constant on one side

Subtract 2 from both sides of the equation to isolate the absolute value, which results in the equation \(|3x+2|=3\).

Solve for when the absolute value content is negative

If the contents of the absolute values are negative, then the equation becomes \(-(3x +2) = 3\). Solving for \(x\) gives \(x = -\frac{5}{3}\)

Solve for when the absolute value content is positive

If the contents of the absolute values are positive, then the equation becomes \(3x +2 = 3\). Solving for \(x\) gives \(x = \frac{1}{3}\).

Check the solutions

Substitute each solution value for \(x\) into the original equation and make sure both sides are balanced. After substituting, both solutions happen to be valid and balance the equation perfectly.