Question

9: circle all of the numbers that are solutions to the following inequality:
\frac{x - 4}{10} \leq -2
a: 0 b: -16 c: -19 d: 14 e: -5 f: -25

Explanation:

Step1: Solve the inequality

Given the inequality \(\frac{x - 4}{10}\leq - 2\). Multiply both sides by 10 to get rid of the denominator: \(x - 4\leq - 2\times10\), which simplifies to \(x - 4\leq - 20\).

Step2: Isolate x

Add 4 to both sides of the inequality: \(x\leq - 20 + 4\), so \(x\leq - 16\).

Step3: Check each option

• Option A: \(0\). Since \(0>-16\), it is not a solution.
• Option B: \(-16\). Since \(-16 = - 16\), it is a solution.
• Option C: \(-19\). Since \(-19<-16\), it is a solution.
• Option D: \(14\). Since \(14>-16\), it is not a solution.
• Option E: \(-5\). Since \(-5>-16\), it is not a solution.
• Option F: \(-25\). Since \(-25<-16\), it is a solution.

Answer:

B: -16, C: -19, F: -25