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Popular >

|(2x+3)/(5x)|<= 1

Solution

\frac{2 x + 3}{5 x} \leq 1

Solution

x \leq - \frac{3}{7} or x \geq 1

+2

Interval Notation

(- \infty, - \frac{3}{7}] \cup [1, \infty)

Decimal Notation

x \leq - 0.42857 \dots or x \geq 1

Solution steps

\frac{2 x + 3}{5 x} \leq 1

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 1 \leq \frac{2 x + 3}{5 x} \leq 1

\frac{2 x + 3}{5 x} \geq - 1 and \frac{2 x + 3}{5 x} \leq 1

(x \leq - \frac{3}{7} or x > 0) and (x < 0 or x \geq 1)

Merge Overlapping Intervals

x \leq - \frac{3}{7} or x \geq 1

Popular Examples

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- ∣ - 2 ∣

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3 x^{2} - 21 x + 36

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\frac{7 + i}{- 6 - 2 i}

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1^{4}

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lo g_{3} (\frac{1}{45})

Frequently Asked Questions (FAQ)

What is |(2x+3)/(5x)|<= 1 ?
The solution to |(2x+3)/(5x)|<= 1 is x<=-3/7 \lor x>= 1