What is |2x-1|+|x|<= 10 ?

The solution to |2x-1|+|x|<= 10 is -3<= x<= 11/3

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|2x-1|+|x|<= 10

∣ 2 x - 1 ∣ + ∣ x ∣ \leq 10

- 3 \leq x \leq \frac{11}{3}

Interval Notation

[- 3, \frac{11}{3}]

Decimal Notation

- 3 \leq x \leq 3.66666 \dots

Solution steps

∣ 2 x - 1 ∣ + ∣ x ∣ \leq 10

Find positive and negative intervals

x < 0, 0 \leq x < \frac{1}{2}, x \geq \frac{1}{2}

Solve the inequality for each interval

- 3 \leq x < 0 or 0 \leq x < \frac{1}{2} or \frac{1}{2} \leq x \leq \frac{11}{3}

Merge Overlapping Intervals

- 3 \leq x \leq \frac{11}{3}

x^{2} - 3 x + x - 2 < 0

∣ x - 3 ∣ - ∣ x - 3 ∣ - ∣ x + 4 ∣ \leq 10

\frac{( x - 3 )}{( x + 1 )} \leq 1

x - 1 - x^{2} \leq x^{2} - 3 x + 4

x^{2} - 5 ∣ x ∣ + 6 < 0