Question

solve the inequality.
|3x + 4| > 6
x < -?/? or x > ?/?

Explanation:

Step1: Apply absolute value inequality rule

For \(|a| > b\) (where \(b>0\)), it is equivalent to \(a < -b\) or \(a > b\). So for \(|3x + 4| > 6\), we get two inequalities:
\(3x + 4 < -6\) or \(3x + 4 > 6\)

Step2: Solve \(3x + 4 < -6\)

Subtract 4 from both sides:
\(3x + 4 - 4 < -6 - 4\)
\(3x < -10\)
Divide both sides by 3:
\(x < -\frac{10}{3}\)

Step3: Solve \(3x + 4 > 6\)

Subtract 4 from both sides:
\(3x + 4 - 4 > 6 - 4\)
\(3x > 2\)
Divide both sides by 3:
\(x > \frac{2}{3}\)

Answer:

\(x < -\frac{10}{3}\) or \(x > \frac{2}{3}\), so the first blank is \(\frac{10}{3}\) and the second blank is \(\frac{2}{3}\)