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

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

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|2x-1|<= 3-x

∣ 2 x - 1 ∣ \leq 3 - x

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

Interval Notation

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

Decimal Notation

- 2 \leq x \leq 1.33333 \dots

Solution steps

∣ 2 x - 1 ∣ \leq 3 - x

Find positive and negative intervals

x < \frac{1}{2}, x \geq \frac{1}{2}

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

2 x^{2} + x = 10

100 = 50 x - 5 x^{2}

12 - 7

∣ - 6 x ∣ = 17

\frac{3 π}{2} = \frac{3}{4}