
b
3
–5≥2 or 
5–b
4
>
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.
 or 



Let's solve the compound inequality step by step:

### First inequality:
\[
\frac{b}{3} - 5 \geq 2
\]
1. Add 5 to both sides:
\[
\frac{b}{3} \geq 7
\]
2. Multiply both sides by 3:
\[
b \geq 21
\]

### Second inequality:
\[
\frac{5 - b}{4} > \frac{1}{2}
\]
1. Multiply both sides by 4 to eliminate the denominator:
\[
5 - b > 2
\]
2. Subtract 5 from both sides:
\[
-b > -3
\]
3. Multiply both sides by -1 (remember to reverse the inequality sign):
\[
b < 3
\]

### Compound inequality:
From the two inequalities, we have:
\[
b \geq 21 \quad \text{or} \quad b < 3
\]

Thus, the solution is:
\[
b < 3 \quad \text{or} \quad b \geq 21
\]

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How do you solve inequalities with fractions and variables?
2. What is the rule for reversing the inequality sign when multiplying by a negative number?
3. How can you graph a compound inequality on a number line?
4. What is the difference between "and" and "or" in compound inequalities?
5. Can compound inequalities ever have overlapping solutions?

**Tip:** Always pay attention to the direction of the inequality when multiplying or dividing by negative numbers!

b/3 - 5 ≥ 2 or (5 - b)/4 > 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.

Discover how to solve compound inequalities like b/3 - 5 ≥ 2 or (5 - b)/4 > 1/2. Learn the step-by-step solution, including the handling of fractions and reversing inequality signs. Suitable for students in Grades 8-10, this problem covers key algebraic concepts.

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