Solved: "Solve absolute value inequality. |3(x−1)+2|≤20"

High School
Algebra
Algebra I
Piecewise-Defined Functions

Paligutanhk

Answered question

2021-12-13

Solve absolute value inequality.

| 3 (x - 1) + 2 | \leq 20

Answer & Explanation

lovagwb

Beginner2021-12-14Added 50 answers

Step 1
Solution -
Given inequality -
$| 3 (x - 1) + 2 | \leq 20$
While solving the mode function, the mode function gives two value, one with positive sign and one with negative sign.
When it gives a value with negative sign, the inequality sign reverses, which means $\leq$ becomes $\geq$ and $\geq$ becomes $\leq$ .
So solving the mode function −
$| 3 (x - 1) + 2 | \leq 20$
$3 (x - 1) + 2 \leq 20$ ...(1)
and
$3 (x - 1) + 2 \geq - 20$ ...(2)
Solving inequality (1) −
$3 (x - 1) + 2 \leq 20$
$3 x - 3 + 2 \leq 20$
$3 x - 1 \leq 20$
$3 x \leq 21$
$x \leq 7$ ...(3)
Solving inequality (2) −
$3 (x - 1) + 2 \geq - 20$
$3 x - 3 + 2 \geq - 20$
$3 x - 1 \geq - 20$
$3 x \geq - 20 + 1$
$3 x \geq - 19$
$x \geq - \frac{19}{3}$ ...(4)
Step 2
Hence from equation (3) and (4),
The value of x must be in the -
$- \frac{19}{3} \leq x \leq 7$

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