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Popular >

|3x-4|+2<= 5

Solution

∣ 3 x - 4 ∣ + 2 \leq 5

Solution

\frac{1}{3} \leq x \leq \frac{7}{3}

+2

Interval Notation

[\frac{1}{3}, \frac{7}{3}]

Decimal Notation

0.33333 \dots \leq x \leq 2.33333 \dots

Solution steps

∣ 3 x - 4 ∣ + 2 \leq 5

Move

2

to the right side

∣ 3 x - 4 ∣ \leq 3

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3 \leq 3 x - 4 \leq 3

3 x - 4 \geq - 3 and 3 x - 4 \leq 3

x \geq \frac{1}{3} and x \leq \frac{7}{3}

Merge Overlapping Intervals

\frac{1}{3} \leq x \leq \frac{7}{3}

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Frequently Asked Questions (FAQ)

What is |3x-4|+2<= 5 ?
The solution to |3x-4|+2<= 5 is 1/3 <= x<= 7/3