Question

solve for b.

$\frac{b}{3}-5geq2$ or $\frac{5 - b}{4}>\frac{1}{2}$

write your answer as a compound inequality like 1 < x < 3 or like x < 1 or x > 3. use integers, decimals, or proper or improper fractions in simplest form.

Explanation:

Step1: Solve the first inequality

Add 5 to both sides of $\frac{b}{3}-5\geq2$.
$\frac{b}{3}-5 + 5\geq2 + 5$, so $\frac{b}{3}\geq7$. Then multiply both sides by 3: $b\geq21$.

Step2: Solve the second inequality

Multiply both sides of $\frac{5 - b}{4}>\frac{1}{2}$ by 4: $5 - b>2$.
Subtract 5 from both sides: $-b>2 - 5$, so $-b>-3$. Multiply both sides by - 1 and reverse the inequality sign: $b < 3$.

Answer:

$b\geq21$ or $b < 3$