Question

question
what is the solution of the following inequality?
|3x + 4| ≤ 7
answer attempt 1 out of 3
{ x | -11/3 ≤ x ≤ 1 }
{ x | x ≤ -1 or x ≥ 11/3 }
{ x | -1 ≤ x ≤ 11/3 }
{ x | x ≤ -11/3 or x ≥ 1 }

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| \leq b\) (where \(b \geq 0\)), it is equivalent to \(-b \leq a \leq b\). So for \(|3x + 4| \leq 7\), we have \(-7 \leq 3x + 4 \leq 7\).

Step2: Solve the left - hand inequality

Subtract 4 from all parts of the compound inequality: \(-7 - 4 \leq 3x+4 - 4\leq 7 - 4\).
Simplify each part: \(-11 \leq 3x \leq 3\).

Step3: Solve for x

Divide all parts of the inequality by 3: \(\frac{-11}{3}\leq\frac{3x}{3}\leq\frac{3}{3}\).
Simplify to get: \(-\frac{11}{3}\leq x \leq 1\).

Answer:

\(\{x|-\frac{11}{3}\leq x \leq 1\}\)