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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

∣ x - 9 ∣ < 0

\frac{m}{3} - 3 \leq - 6

simplify f(g^{-1}(15/17))simplify

f (g^{- 1} (\frac{15}{17}))

factor 28x^3+88x^2-37x-7 factor

28 x^{3} + 88 x^{2} - 37 x - 7

simplify 9sqrt(63)simplify

963

Frequently Asked Questions (FAQ)

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