What is (2x-3)/(4x-5)<= 1 ?

The solution to (2x-3)/(4x-5) 5/4

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(2x-3)/(4x-5)<= 1

\frac{2 x - 3}{4 x - 5} \leq 1

x \leq 1 or x > \frac{5}{4}

Interval Notation

(- \infty, 1] \cup (\frac{5}{4}, \infty)

Decimal Notation

x \leq 1 or x > 1.25

Solution steps

\frac{2 x - 3}{4 x - 5} \leq 1

Rewrite in standard form

\frac{- 2 x + 2}{4 x - 5} \leq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Divide both sides by

2

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

Simplify

\frac{x - 1}{4 x - 5} \geq 0

Identify the intervals

x \leq 1 or x > \frac{5}{4}

3 x y - 4 x - 9 y + 12

(8)^{\frac{1}{2}}

36 x^{2} - 36 x

\frac{( - 7 ) ^{8}}{( - 7 ) ^{6}}

x (x - 1) (x + 8) > 0

What is (2x-3)/(4x-5)<= 1 ?
The solution to (2x-3)/(4x-5)<= 1 is x<= 1\lor x> 5/4