What is (x+1)/(x-3)<= 5 ?

The solution to (x+1)/(x-3) = 4

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

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

x < 3 or x \geq 4

Interval Notation

(- \infty, 3) \cup [4, \infty)

Solution steps

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

Rewrite in standard form

\frac{- 4 x + 16}{x - 3} \leq 0

Factor

\frac{- 4 x + 16}{x - 3} : \frac{- 4 ( x - 4 )}{x - 3}

\frac{- 4 ( x - 4 )}{x - 3} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 4 ( x - 4 ) ) ( - 1 )}{x - 3} \geq 0 \cdot (- 1)

Simplify

\frac{4 ( x - 4 )}{x - 3} \geq 0

Divide both sides by

4

\frac{\frac{4 ( x - 4 )}{x - 3}}{4} \geq \frac{0}{4}

Simplify

\frac{x - 4}{x - 3} \geq 0

Identify the intervals

x < 3 or x \geq 4

6 n - 2 (4 n + 7) + 4 = - 2

312 + 775 - 54

(x - 3) (x + 4) = 0

6 - 2

\frac{2 ^{3}}{2 ^{2}}