Question

Solve for x −9x+5≤17 OR 13x+25≤−1

Answer 1

Answer:

$(-\infty,-2] \cup [\displaystyle\frac{-4}{3},-\infty)$

Step-by-step explanation:

We are given the following information in the question:

We have to solve the given inequalities for x:

Inequality 1

$-9x+5 \leq 17\\-9x \leq 17-5\\-9x \leq 12\\\\x \leq \displaystyle\frac{12}{-9}\\\\x \geq \frac{-4}{3}\\\\x \in [\frac{-4}{3},-\infty)$

Inequality 2

$13x + 25 \leq -1\\13x \leq -1-25\\13x \leq -26\\\\x \leq \displaystyle\frac{-26}{13}\\\\x \leq -2\\x \in (-\infty,-2]$

The combined solution for both the inequalities is given by:

$(-\infty,-2] \cup [\displaystyle\frac{-4}{3},-\infty)$

Answer 2

Answer:

(-∞ 2] ∪ [-4/3 ∞ )

Step-by-step explanation:

Given compound inequality,

$-9x+5\leq 17\text{ or }13x+25\leq -1$

$-9x\leq 12\text{ or }13x\leq -26$  ( Subtraction property of inequality )

$-x\leq \frac{12}{9}\text{ or }x\leq -\frac{26}{13}$   ( Division property of inequality )

$-x\leq \frac{4}{3}\text{ or }x\leq -2$

$x\geq -\frac{4}{3}\text{ or }x\leq -2$   ( a < b ⇒ - a > - b )

Hence, the solution of the given inequality is,

(-∞ -2] ∪ [-4/3 ∞ )