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Popular >

(x+1)/(x-5)<3

Solution

\frac{x + 1}{x - 5} < 3

Solution

x < 5 or x > 8

+1

Interval Notation

(- \infty, 5) \cup (8, \infty)

Solution steps

\frac{x + 1}{x - 5} < 3

Rewrite in standard form

\frac{- 2 x + 16}{x - 5} < 0

Factor

\frac{- 2 x + 16}{x - 5} : \frac{- 2 ( x - 8 )}{x - 5}

\frac{- 2 ( x - 8 )}{x - 5} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( x - 8 ) ) ( - 1 )}{x - 5} > 0 \cdot (- 1)

Simplify

\frac{2 ( x - 8 )}{x - 5} > 0

Divide both sides by

2

\frac{\frac{2 ( x - 8 )}{x - 5}}{2} > \frac{0}{2}

Simplify

\frac{x - 8}{x - 5} > 0

Identify the intervals

x < 5 or x > 8

Popular Examples

5 x + 2 \leq 17

simplify |x+iy|^2 simplify

∣ x + i y ∣^{2}

13 x - 9 = 10 x + 18

factor 3x^2-15x+12 factor

3 x^{2} - 15 x + 12

factor 28a^2+5ab-12b^2 factor

28 a^{2} + 5 ab - 12 b^{2}

Frequently Asked Questions (FAQ)

What is (x+1)/(x-5)<3 ?
The solution to (x+1)/(x-5)<3 is x<5\lor x>8