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Popular >

(4x-5)/(7x)<2

Solution

\frac{4 x - 5}{7 x} < 2

Solution

x < - \frac{1}{2} or x > 0

+2

Interval Notation

(- \infty, - \frac{1}{2}) \cup (0, \infty)

Decimal Notation

x < - 0.5 or x > 0

Solution steps

\frac{4 x - 5}{7 x} < 2

Rewrite in standard form

\frac{- 10 x - 5}{x} < 0

Factor

\frac{- 10 x - 5}{x} : \frac{- 5 ( 2 x + 1 )}{x}

\frac{- 5 ( 2 x + 1 )}{x} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 5 ( 2 x + 1 ) ) ( - 1 )}{x} > 0 \cdot (- 1)

Simplify

\frac{5 ( 2 x + 1 )}{x} > 0

Divide both sides by

5

\frac{\frac{5 ( 2 x + 1 )}{x}}{5} > \frac{0}{5}

Simplify

\frac{2 x + 1}{x} > 0

Identify the intervals

x < - \frac{1}{2} or x > 0

Popular Examples

4 x - 8 \geq 4

simplify 1/a-1/b simplify

\frac{1}{a} - \frac{1}{b}

simplify 3(-1/2)simplify

3 (- \frac{1}{2})

(x+3)^2+8(x+3)-9=0

(x + 3)^{2} + 8 (x + 3) - 9 = 0

x - 7 > - 11

Frequently Asked Questions (FAQ)

What is (4x-5)/(7x)<2 ?
The solution to (4x-5)/(7x)<2 is x<-1/2 \lor x>0