Question

The solution set for all real numbers x such that 2x + 3 < 19 and 2x − 3 ≤ -7 is (, ].

Note: If needed, type “-infinity” for -∞ and “infinity” for ∞.

Answer 1

Solve each inequality separately:

1.
`2x+3<19.`

Subtract 3 from both sides of the inequality

`2x+3-3<19-3,\\ \\2x<16.`

Divide the inequality by 2

`x<8.`

2.
`2x-3\le -7.`

Add 3 to both sides of the inequality

`2x-3+3\le -7+3,\\ \\2x\le -4.`

Divide the inequality by 2

`x\le -2.`

3. The solution set for the system of two inequalities is

`x\le -2`

or in other words
`(-\infty,-2].`

Answer:
`(-\infty,-2].`