solve for x −9x+5≤17 OR 13x+25≤−1

Question

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Respuesta :

slicergiza slicergiza · Answer 1 · 2019-07-19T20:19:07+02:00

Answer:

(-∞ 2] ∪ [-4/3 ∞ )

Step-by-step explanation:

Given compound inequality,

[tex]-9x+5\leq 17\text{ or }13x+25\leq -1[/tex]

[tex]-9x\leq 12\text{ or }13x\leq -26[/tex] ( Subtraction property of inequality )

[tex]-x\leq \frac{12}{9}\text{ or }x\leq -\frac{26}{13}[/tex] ( Division property of inequality )

[tex]-x\leq \frac{4}{3}\text{ or }x\leq -2[/tex]

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

Hence, the solution of the given inequality is,

(-∞ -2] ∪ [-4/3 ∞ )

ChiKesselman ChiKesselman · Answer 2 · 2019-11-04T20:13:04+01:00

Answer:

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

Step-by-step explanation:

We are given the following information in the question:

We have to solve the given inequalities for x:

Inequality 1

[tex]-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)[/tex]

Inequality 2

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

The combined solution for both the inequalities is given by:

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