Question

solve for g.
$5g - 1 < 19$ or $\frac{3g - 2}{2} > 8$
write your answer as a compound inequality with integers.

Explanation:

Step1: Solve \(5g - 1 < 19\)

Add 1 to both sides: \(5g - 1 + 1 < 19 + 1\)
Simplify: \(5g < 20\)
Divide both sides by 5: \(\frac{5g}{5} < \frac{20}{5}\)
Simplify: \(g < 4\)

Step2: Solve \(\frac{3g - 2}{2} > 8\)

Multiply both sides by 2: \(2\times\frac{3g - 2}{2} > 8\times2\)
Simplify: \(3g - 2 > 16\)
Add 2 to both sides: \(3g - 2 + 2 > 16 + 2\)
Simplify: \(3g > 18\)
Divide both sides by 3: \(\frac{3g}{3} > \frac{18}{3}\)
Simplify: \(g > 6\)

Answer:

\(g < 4\) or \(g > 6\)