What is (10-x)/(4x-7)<5 ?

The solution to (10-x)/(4x-7) 15/7

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

\frac{10 - x}{4 x - 7} < 5

x < \frac{7}{4} or x > \frac{15}{7}

Solution steps

\frac{10 - x}{4 x - 7} < 5

Rewrite in standard form

\frac{- 21 x + 45}{4 x - 7} < 0

Factor

\frac{- 21 x + 45}{4 x - 7} : \frac{- 3 ( 7 x - 15 )}{4 x - 7}

\frac{- 3 ( 7 x - 15 )}{4 x - 7} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 3 ( 7 x - 15 ) ) ( - 1 )}{4 x - 7} > 0 \cdot (- 1)

Simplify

\frac{3 ( 7 x - 15 )}{4 x - 7} > 0

Divide both sides by

3

\frac{\frac{3 ( 7 x - 15 )}{4 x - 7}}{3} > \frac{0}{3}

Simplify

\frac{7 x - 15}{4 x - 7} > 0

Identify the intervals

x < \frac{7}{4} or x > \frac{15}{7}

z^{5} - 15 = - 17

781

- 5 a^{2} + 20 a - 120

r^{2} - 11 r + 18

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

What is (10-x)/(4x-7)<5 ?
The solution to (10-x)/(4x-7)<5 is x< 7/4 \lor x> 15/7