Question

u2: solve the absolute value inequality |x + 7| < 12, and write the answer in inequality notation.

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| < B\) (where \(B>0\)), it is equivalent to \(-B < A < B\). Here, \(A = x + 7\) and \(B = 12\) (and \(12>0\)), so we can rewrite the inequality as:
\(-12 < x + 7 < 12\)

Step2: Solve for \(x\) by subtracting 7

Subtract 7 from all parts of the compound inequality:
\(-12 - 7 < x + 7 - 7 < 12 - 7\)
Simplify each part:
\(-19 < x < 5\)

Answer:

\(-19 < x < 5\)