Question

Solve the equation. $$|3 x+5|=23$$

Short answer

The solutions to the equation are \(x=6\) and \(x=-28/3\).

Step-by-step solution

Equation from positive absolute value

First, consider the equation where the absolute value expression equals a positive number, which is \(3x+5=23\). To solve for x, first subtract 5 from both sides of the equation to isolate the term with x, which is \(3x=18\). Then, divide both sides of the equation by 3 to solve for x: \(x=6\).

Equation from negative absolute value

Next, consider the equation where the absolute value expression equals a negative number, which is \(3x+5=-23\). Just like the previous step, first subtract 5 from both sides of the equation to isolate the term with x, which is \(3x=-28\). Then, divide both sides of the equation by 3 to find that \(x=-28/3\) which approximates -9.33.

Final Answer

The solutions to the given absolute value equation are the solutions to the two derived equations, which are \(x=6\) and \(x=-28/3\).