What is the solution to the compound inequality 5x + 7 ≥ −8 and 3x + 7 < 19?

Mathematics · High School · Mon Jan 18 2021

Answered on

Given the inequalities:

5x + 7 ≥ −8 

3x + 7 < 19

Determine the solution.

Solution:

In order to determine the solution of each inequality, we solve for the values of x separately.

5x + 7 ≥ −8

Transpose 7 on the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

5x ≥ −8  - 7

5x ≥ −15

Divide both sides by 5 in order to determine the value of x.

5x/5 ≥ −15/5

x ≥ -3

3x + 7 < 19

Do the same process of transposing and dividing by 3 in order to determine the value of x.

3x < 19 - 7

3x < 12

3x/3 < 12

x < 4

Final answer:

x ≥ -3

x < 4