Question

Solve for x −9x+5≤17 OR 13x+25≤−1

Answer 1

`(-\infty,-2] \cup [\displaystyle(-4)/(3),-\infty)`

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(12)/(-9)\\\\x \geq (-4)/(3)\\\\x \in [(-4)/(3),-\infty)`

Inequality 2

`13x + 25 \leq -1\\13x \leq -1-25\\13x \leq -26\\\\x \leq \displaystyle(-26)/(13)\\\\x \leq -2\\x \in (-\infty,-2]`

The combined solution for both the inequalities is given by:

`(-\infty,-2] \cup [\displaystyle(-4)/(3),-\infty)`

Answer 2

(-∞ 2] ∪ [-4/3 ∞ )

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

`-x\leq (4)/(3)\text{ or }x\leq -2`

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

Hence, the solution of the given inequality is,

(-∞ -2] ∪ [-4/3 ∞ )