Question

The inequalities (1/5)x + 7 ≤ 11 and (–1/5)x – 7 ≥ –11 have the same solutions. What are the solutions for both inequalities? Explain your reasoning. *

Part 2
Without performing any calculations, how can you tell that inequalities will have the same solutions? *

Answer 1

To solve the inequalities, we need to move

linear to left, constant to right.

Part 1

The solutions of two inequalities are same. (On Part 2)

(1/5)x + 7 ≤ 11

(1/5)x + 7 - 7 ≤ 11 - 7

5 * (1/5)x  ≤ 11 * 5

x ≤ 55 is the solution.

Part 2

We can show that by multiplying -1 on both sides,

change the direction of inequality.

(–1/5)x – 7 ≥ –11

(-1) * (–1/5)x – 7 ≥ –11 * (-1)

(1/5)x + 7 ≤ 11

It gives the same inequality.

So the inequality will have same solution.