Question

solve the inequality and read carefully to answe
7: which are solutions to the following inequality?
\\(\frac{3}{4}x - 6 < 12\\)
a: 21 b: 22 c: 23 d: 24 e: 25

Explanation:

Step1: Solve the inequality

Start with the inequality $\frac{3}{4}x - 6 < 12$. Add 6 to both sides: $\frac{3}{4}x - 6 + 6 < 12 + 6$, which simplifies to $\frac{3}{4}x < 18$. Then multiply both sides by $\frac{4}{3}$: $\frac{3}{4}x \times \frac{4}{3} < 18 \times \frac{4}{3}$. This gives $x < 24$.

Step2: Check each option

• Option A: 21 < 24, so 21 is a solution.
• Option B: 22 < 24, so 22 is a solution.
• Option C: 23 < 24, so 23 is a solution.
• Option D: 24 is not less than 24, so 24 is not a solution.
• Option E: 25 > 24, so 25 is not a solution.

Answer:

A. 21, B. 22, C. 23