Question

A student solves the compound inequality 15 ≤ 2x + 5 ≤ 17 and finds the solutions of the compound inequality to be all real numbers. Explain and correct the student's mistake.

Answer 1

Answer:

The solutions of the compound inequality is 5 ≤ x  ≤ 6

Step-by-step explanation:

A compound inequality is two or more inequalities joined. For its resolution, each inequality must be solved separately. In the case of 15 ≤ 2x + 5 ≤ 17, you have:

Inequality (A) 15 ≤ 2x + 5 and Inequality (B) 2x + 5 ≤ 17

The solution of the inequalities consists of finding the value that the unknown x must take for the inequality to be fulfilled, passing all the terms with x to one member (for example to the first member), and all the numbers (terms without x) to the other member through the opposite operation (The opposite operation to addition is subtraction and vice versa, and the opposite operation to multiplication is division and vice versa). In this case, solving the inequalities:

Inequality (A) 15 ≤ 2x + 5

15 - 5 ≤ 2x

10 ≤ 2x

10÷2 ≤ x

5 ≤ x

Inequality (B) 2x + 5 ≤ 17

2x ≤ 17 -5

2x ≤ 12

x ≤ 12÷2

x ≤ 6

The solution of a compound inequality are all the solutions that have in  common the two inequalities. Graphically, it is as if they were two graphs that overlap.

So, in this case the solutions of the compound inequality is 5 ≤ x  ≤ 6

In the image you can see the solution to the compound inequality.