What is 1/3 |3x-1|-3<= 5 ?

The solution to 1/3 |3x-1|-3<= 5 is -23/3 <= x<= 25/3

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1/3 |3x-1|-3<= 5

\frac{1}{3} ∣ 3 x - 1 ∣ - 3 \leq 5

- \frac{23}{3} \leq x \leq \frac{25}{3}

Interval Notation

[- \frac{23}{3}, \frac{25}{3}]

Decimal Notation

- 7.66666 \dots \leq x \leq 8.33333 \dots

Solution steps

\frac{1}{3} ∣ 3 x - 1 ∣ - 3 \leq 5

Move

3

to the right side

\frac{1}{3} ∣ 3 x - 1 ∣ \leq 8

Multiply both sides by

3

∣ 3 x - 1 ∣ \leq 24

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 24 \leq 3 x - 1 \leq 24

3 x - 1 \geq - 24 and 3 x - 1 \leq 24

x \geq - \frac{23}{3} and x \leq \frac{25}{3}

Merge Overlapping Intervals

- \frac{23}{3} \leq x \leq \frac{25}{3}

\frac{1}{11} x^{2} - 11 = 0

\frac{2 3}{6}

3 x^{4} - 15 n^{3} + 12 n^{2}

∣ x - 7 ∣ \geq 8

2^{23}

What is 1/3 |3x-1|-3<= 5 ?
The solution to 1/3 |3x-1|-3<= 5 is -23/3 <= x<= 25/3