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