What is 1<= (4x-5)/(-2)<9 ?

The solution to 1<= (4x-5)/(-2)<9 is -13/4 <x<= 3/4

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1<= (4x-5)/(-2)<9

1 \leq \frac{4 x - 5}{- 2} < 9

- \frac{13}{4} < x \leq \frac{3}{4}

Interval Notation

(- \frac{13}{4}, \frac{3}{4}]

Decimal Notation

- 3.25 < x \leq 0.75

Solution steps

1 \leq \frac{4 x - 5}{- 2} < 9

a \leq u < b

then

a \leq u and u < b

1 \leq \frac{4 x - 5}{- 2} and \frac{4 x - 5}{- 2} < 9

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

\frac{4 x - 5}{- 2} < 9 : x > - \frac{13}{4}

Combine the intervals

x \leq \frac{3}{4} and x > - \frac{13}{4}

Merge Overlapping Intervals

- \frac{13}{4} < x \leq \frac{3}{4}

\frac{3 x - 5}{4} = \frac{x + 1}{2}

1 > \frac{q}{2} - 1

\frac{m ^{2}}{100} = \frac{1}{2}

3 \cdot 9

- 8 x + 14 \geq 60