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

The solution to |3x-1|-3<= | x/2+1| is -6/7 <= x<= 2

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

∣ 3 x - 1 ∣ - 3 \leq \frac{x}{2} + 1

- \frac{6}{7} \leq x \leq 2

Interval Notation

[- \frac{6}{7}, 2]

Decimal Notation

- 0.85714 \dots \leq x \leq 2

Solution steps

∣ 3 x - 1 ∣ - 3 \leq \frac{x}{2} + 1

Find positive and negative intervals

x < - 2, - 2 \leq x < \frac{1}{3}, x \geq \frac{1}{3}

Solve the inequality for each interval

No Solution or - \frac{6}{7} \leq x < \frac{1}{3} or \frac{1}{3} \leq x \leq 2

Merge Overlapping Intervals

- \frac{6}{7} \leq x \leq 2

e^{1} - e^{0}

1 + (a - 3 b)^{3}

x + \frac{1}{4} = \frac{7}{8}

\frac{a ^{6}}{a ^{4}}

\frac{2}{3} = \frac{x}{12}

What is |3x-1|-3<= | x/2+1| ?
The solution to |3x-1|-3<= | x/2+1| is -6/7 <= x<= 2