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Popular >

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

Solution

\frac{∣ 2 x + 3 ∣}{5 x} \leq 1

Solution

x < 0

+1

Interval Notation

(- \infty, 0)

Solution steps

\frac{∣ 2 x + 3 ∣}{5 x} \leq 1

Move

1

to the left side

\frac{∣ 2 x + 3 ∣}{5 x} - 1 \leq 0

∣ 2 x + 3 ∣ \geq 0

If

\frac{a}{b} \leq 0 and a \geq 0

then

b < 0 or a = 0

5 x < 0 or ∣ 2 x + 3 ∣ = 0

5 x < 0 : x < 0

∣ 2 x + 3 ∣ = 0 : x = - \frac{3}{2}

Combine the intervals

x < 0 or x = - \frac{3}{2}

Merge Overlapping Intervals

x < 0

Popular Examples

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(\frac{2}{3})^{- 4} m^{- 5} n^{- 2}

\frac{1}{4} (4)^{0}

∣ x - 7 ∣ = 24

- 8 < \frac{y}{5}

- \frac{3}{7} x = \frac{12}{35}

Frequently Asked Questions (FAQ)

What is (|2x+3|)/(5x)<= 1 ?
The solution to (|2x+3|)/(5x)<= 1 is x<0