Using the properties of inequality, justify both steps in solving the inequality: 3/5x+6≥36

Question

What is the solution to the inequality?(1 point)

Answer 1

To solve the inequality \( \frac{3}{5}x + 6 \geq 36 \), we will follow these steps, justifying each step using the properties of inequality.

1. Subtract 6 from both sides: \[ \frac{3}{5}x + 6 - 6 \geq 36 - 6 \] This simplifies to: \[ \frac{3}{5}x \geq 30 \] Justification: According to the properties of inequalities, subtracting the same number from both sides of an inequality does not change the direction of the inequality.

2. Multiply both sides by \(\frac{5}{3}\) (the reciprocal of \(\frac{3}{5}\)): \[ \frac{5}{3} \cdot \frac{3}{5}x \geq 30 \cdot \frac{5}{3} \] This simplifies to: \[ x \geq 50 \] Justification: When we multiply both sides of an inequality by a positive number, the direction of the inequality remains the same.

Solution

The solution to the inequality is: \[ x \geq 50 \]