Solve the compound inequality. 4x+1≥21 and 3x−2≤−17 Write the solution in interval notation.

Step 1 We first solve for x from 4x+1≥21 4x+1≥21 4x+1−1≥21−1 4x≥20 x≥204 x≥5 Step 2 Then we find x from 3x−2≤−17 3x−2≤−17 3x−2+2≤−17+2 3x≤−15 x≤−153 x≤−5 Step 3 Combining x≥5 and x≤−5 we get solution region =(−∞,−5]⋃[5,∞) Answer: (−∞,−5]⋃[5,∞)

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High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Dillard

Answered question

2021-09-30

Solve the compound inequality.

4 x + 1 \geq 21

and

3 x - 2 \leq - 17

Write the solution in interval notation.

Answer & Explanation

yagombyeR

Skilled2021-10-01Added 92 answers

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

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