Solve the compound inequality 2x – 3 < 7 and 5 – x ≤ 8.

[-3,5)

Step-by-step explanation:

Compound inequality

2x - 3 < 7

And

5 - x ≤ 8

The solution is the conjunction of the individual solutions because both conditions must be met.

From the first inequality we get:

2x < 7 + 3

2x < 10

x < 5

From the second inequality we get:

- x ≤ 8 - 5

- x ≤ 3

Multiplying by -1 and flipping the sign:

x ≥ -3

Thus the solution is the set of numbers that lie in the interval [-3,5)

d. vertex

step-by-step explanation:

x + 4/7

step-by-step explanation:

use cymath