Question

Solve the two-step inequality
3/4x−10≤2

Answer 1

To solve the inequality \( \frac{3}{4}x - 10 \leq 2 \), follow these steps:

1. **Isolate the term with \( x \)**:
Add 10 to both sides of the inequality:
\[
\frac{3}{4}x - 10 + 10 \leq 2 + 10
\]
Simplifying this gives:
\[
\frac{3}{4}x \leq 12
\]

2. **Eliminate the fraction**:
Multiply both sides by \( \frac{4}{3} \) to solve for \( x \). Note that multiplying by a positive number does not change the direction of the inequality:
\[
x \leq 12 \times \frac{4}{3}
\]
Calculating the right side:
\[
x \leq 16
\]

The solution to the inequality is:
\[
x \leq 16
\]