What is | 3/2 x-2|+1<= 2 ?

The solution to | 3/2 x-2|+1<= 2 is 2/3 <= x<= 2

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| 3/2 x-2|+1<= 2

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

\frac{2}{3} \leq x \leq 2

Interval Notation

[\frac{2}{3}, 2]

Decimal Notation

0.66666 \dots \leq x \leq 2

Solution steps

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

Move

1

to the right side

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

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

\frac{3}{2} x - 2 \geq - 1 and \frac{3}{2} x - 2 \leq 1

x \geq \frac{2}{3} and x \leq 2

Merge Overlapping Intervals

\frac{2}{3} \leq x \leq 2

- 1 - \frac{4}{3}

1^{1}

m^{2} + 18 m - 3 = 0

ln (9) - ln (3)

(8 m + 12)^{2} = 4