Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not cou
find the solution to the absolute value inequality $-3|x - 4| < 6$. (1 point)
\bigcirc (2,6)
\bigcirc no solution
\bigcirc $(-\infty, 2) \cup (6, \infty)$
\bigcirc $(-\infty, \infty)$

Explanation:

Step1: Divide both sides by -3

When dividing an inequality by a negative number, the inequality sign flips. So we have \(\frac{-3|x - 4|}{-3}>\frac{6}{-3}\), which simplifies to \(|x - 4|>- 2\).

Step2: Analyze the absolute value

The absolute value of any real number \(a\), \(|a|\), is always greater than or equal to 0. So \(|x - 4|\) is always greater than or equal to 0, and since 0 is greater than - 2, the inequality \(|x - 4|>-2\) is true for all real numbers \(x\). That means the solution set is all real numbers, which is \((-\infty,\infty)\).

Answer:

\((-\infty,\infty)\) (the last option: \((-\infty,\infty)\))