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

The solution to |3x-2|<= x+1 is 1/4 <= x<= 3/2

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|3x-2|<= x+1

∣ 3 x - 2 ∣ \leq x + 1

\frac{1}{4} \leq x \leq \frac{3}{2}

Interval Notation

[\frac{1}{4}, \frac{3}{2}]

Decimal Notation

0.25 \leq x \leq 1.5

Solution steps

∣ 3 x - 2 ∣ \leq x + 1

Find positive and negative intervals

x < \frac{2}{3}, x \geq \frac{2}{3}

Solve the inequality for each interval

\frac{1}{4} \leq x < \frac{2}{3} or \frac{2}{3} \leq x \leq \frac{3}{2}

Merge Overlapping Intervals

\frac{1}{4} \leq x \leq \frac{3}{2}

∣ x - 2 ∣ + ∣ x - 1 ∣ > 1

∣ 2 + 3 x ∣ > 0

\frac{( x ^{2} - 1 )}{( 3 - 2 x - x ^{2} )} \leq 1

∣ 4 x - 5 ∣ > 8

\frac{( x + 2 )}{5} < 1