X+7 less than or equal to -2 or x+7 greater than or equal to -3

Question

asked May 12, 2023 37.8k views

1 Answer

Flyingfoxlee · Answer 1 · 2023-05-18T17:22:32+0000

$-10\le x\le-9$

Given the following inequality expressions:

$x+7\leq-2\text{ or }x+7\ge-3$

The inequality expression x + 7 ≥ - 3 can be written as -3 ≤ x + 7.

Combine -3 ≤ x + 7 with x + 7 ≤ -2 to have:

$-3\leq x+7\leq-2$

Subtract 7 from all the sides to have:

$\begin{gathered} -3-7\leq x+7-7\leq-2-7 \\ -10\leq x\leq-9 \end{gathered}$

Hence the solution to the system of inequalities is -10 ≤ x ≤ -9