Question

solve the absolute value equation for x. write your answer in inequality notation. 3|x| - 3 < 15 show your work here hint: to add inequalities enter your answer

Explanation:

Step1: Isolate the absolute value

Start with the inequality \( 3|x| - 3 < 15 \). Add 3 to both sides to isolate the absolute value term:
\( 3|x| - 3 + 3 < 15 + 3 \)
Simplify: \( 3|x| < 18 \).

Step2: Divide by the coefficient

Divide both sides by 3 to solve for \( |x| \):
\( \frac{3|x|}{3} < \frac{18}{3} \)
Simplify: \( |x| < 6 \).

Step3: Solve the absolute value inequality

The inequality \( |x| < 6 \) means \( x \) is between -6 and 6. In interval notation, this is \( -6 < x < 6 \).

Answer:

\( -6 < x < 6 \)