What is 3/(4x)-6<= x-7 ?

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3/(4x)-6<= x-7

\frac{3}{4 x} - 6 \leq x - 7

- \frac{1}{2} \leq x < 0 or x \geq \frac{3}{2}

Interval Notation

[- \frac{1}{2}, 0) \cup [\frac{3}{2}, \infty)

Decimal Notation

- 0.5 \leq x < 0 or x \geq 1.5

Solution steps

\frac{3}{4 x} - 6 \leq x - 7

Rewrite in standard form

\frac{3 + 4 x - 4 x ^{2}}{x} \leq 0

Factor

\frac{3 + 4 x - 4 x ^{2}}{x} : \frac{- ( 2 x + 1 ) ( 2 x - 3 )}{x}

\frac{- ( 2 x + 1 ) ( 2 x - 3 )}{x} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 2 x + 1 ) ( 2 x - 3 ) ) ( - 1 )}{x} \geq 0 \cdot (- 1)

Simplify

\frac{( 2 x + 1 ) ( 2 x - 3 )}{x} \geq 0

Identify the intervals

- \frac{1}{2} \leq x < 0 or x \geq \frac{3}{2}

\frac{12 !}{0 ! 12 !} (0.36)^{12} (0.64)^{0}

ln (1.06)

1960

\frac{7}{2} + 4

9 p^{2} + 10 p - 3 = - 7

What is 3/(4x)-6<= x-7 ?
The solution to 3/(4x)-6<= x-7 is -1/2 <= x<0\lor x>= 3/2