What is (14)/(5+4x)<= 7 ?

The solution to (14)/(5+4x) =-3/4

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(14)/(5+4x)<= 7

\frac{14}{5 + 4 x} \leq 7

x < - \frac{5}{4} or x \geq - \frac{3}{4}

Interval Notation

(- \infty, - \frac{5}{4}) \cup [- \frac{3}{4}, \infty)

Decimal Notation

x < - 1.25 or x \geq - 0.75

Solution steps

\frac{14}{5 + 4 x} \leq 7

Rewrite in standard form

\frac{- 28 x - 21}{5 + 4 x} \leq 0

Factor

\frac{- 28 x - 21}{5 + 4 x} : \frac{- 7 ( 4 x + 3 )}{5 + 4 x}

\frac{- 7 ( 4 x + 3 )}{5 + 4 x} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 7 ( 4 x + 3 ) ) ( - 1 )}{5 + 4 x} \geq 0 \cdot (- 1)

Simplify

\frac{7 ( 4 x + 3 )}{5 + 4 x} \geq 0

Divide both sides by

7

\frac{\frac{7 ( 4 x + 3 )}{5 + 4 x}}{7} \geq \frac{0}{7}

Simplify

\frac{4 x + 3}{5 + 4 x} \geq 0

Identify the intervals

x < - \frac{5}{4} or x \geq - \frac{3}{4}

\frac{r}{10} + 4 = 5

\frac{1}{2} + \frac{1}{3} + \frac{1}{5}

x^{2} - 2 x - 63 < 0

j + 6 < 9

18 n^{3} - 9 n^{2} + 10 n - 5

What is (14)/(5+4x)<= 7 ?
The solution to (14)/(5+4x)<= 7 is x<-5/4 \lor x>=-3/4