What is |3(x-1)+2|<= 20 ?

The solution to |3(x-1)+2|<= 20 is -19/3 <= x<= 7

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|3(x-1)+2|<= 20

∣ 3 (x - 1) + 2 ∣ \leq 20

- \frac{19}{3} \leq x \leq 7

Interval Notation

[- \frac{19}{3}, 7]

Decimal Notation

- 6.33333 \dots \leq x \leq 7

Solution steps

∣ 3 (x - 1) + 2 ∣ \leq 20

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

3 (x - 1) + 2 \geq - 20 and 3 (x - 1) + 2 \leq 20

x \geq - \frac{19}{3} and x \leq 7

Merge Overlapping Intervals

- \frac{19}{3} \leq x \leq 7

ln (x y)

2 (4 u - 7) = 66

81 x^{2} - 36 = 0

\frac{x}{3 x - 5} \leq \frac{2}{x - 1}

0 = 8 x^{2} - 800