What is (10-4x)/(2x-5)>= 4x-1 ?

The solution to (10-4x)/(2x-5)>= 4x-1 is x<=-1/4

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(10-4x)/(2x-5)>= 4x-1

\frac{10 - 4 x}{2 x - 5} \geq 4 x - 1

x \leq - \frac{1}{4}

Interval Notation

(- \infty, - \frac{1}{4}]

Decimal Notation

x \leq - 0.25

Solution steps

\frac{10 - 4 x}{2 x - 5} \geq 4 x - 1

Rewrite in standard form

\frac{- 8 x ^{2} + 18 x + 5}{2 x - 5} \geq 0

Factor

\frac{- 8 x ^{2} + 18 x + 5}{2 x - 5} : \frac{- ( 4 x + 1 ) ( 2 x - 5 )}{2 x - 5}

\frac{- ( 4 x + 1 ) ( 2 x - 5 )}{2 x - 5} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 4 x + 1 ) ( 2 x - 5 ) ) ( - 1 )}{2 x - 5} \leq 0 \cdot (- 1)

Simplify

\frac{( - ( 4 x + 1 ) ( 2 x - 5 ) ) ( - 1 )}{2 x - 5} : 4 x + 1

4 x + 1 \leq 0

Identify the intervals

x \leq - \frac{1}{4}

x^{2} + 4 x + 21 = 42

9 (3 x + 9) + (x + 3) = 14

\frac{\frac{2 x + y}{36}}{\frac{36 + 36 x - 7 x ^{2}}{288}}

- \frac{11}{2 ( - 3 + 4 ) ^{2}}

392

What is (10-4x)/(2x-5)>= 4x-1 ?
The solution to (10-4x)/(2x-5)>= 4x-1 is x<=-1/4