Question

Solve the compound inequality 7x ≥ –56 and 9x < 54

Answer 1

For the first inequality- (-8)

Second inequality- 6

Explanation:

First inequality- divide both sides by 7.

Second inequality- divide both sides by 9

Hope this helps ^-^

Answer 2

The intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6.

Solving compound inequalities.

A compound inequality is the joining of two or more inequalities together and they are united by the word (and) or (or). In the given compound inequality, we have:

7x ≥ - 56 and 9x < 54.

Solving the compound inequality, we have;
7x ≥ - 56

Divide both sides by 7

`(7x)/(7) \geq (56)/(7)`

x ≥ 8

Also, 9x < 54

Divide both sides by 9.

`(9x)/(9) < (54)/(9)`

x < 6.

Therefore, the intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6