Dillard

2021-09-30

Solve the compound inequality.
$4x+1\ge 21$ and $3x-2\le -17$
Write the solution in interval notation.

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yagombyeR

Expert

Step 1
We first solve for x from $4x+1\ge 21$
$4x+1\ge 21$
$4x+1-1\ge 21-1$
$4x\ge 20$
$x\ge \frac{20}{4}$
$x\ge 5$
Step 2
Then we find x from $3x-2\le -17$
$3x-2\le -17$
$3x-2+2\le -17+2$
$3x\le -15$
$x\le \frac{-15}{3}$
$x\le -5$
Step 3
Combining $x\ge 5$ and $x\le -5$ we get solution region $=\left(-\mathrm{\infty },-5\right]\bigcup \left[5,\mathrm{\infty }\right)$
Answer: $\left(-\mathrm{\infty },-5\right]\bigcup \left[5,\mathrm{\infty }\right)$

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