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

The solution to -1<= (2x-3)/2 <4 is 1/2 <= x< 11/2

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

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

\frac{1}{2} \leq x < \frac{11}{2}

Interval Notation

Decimal

0.5 \leq x < 5.5

Solution steps

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

a \leq u < b

then

a \leq u and u < b

- 1 \leq \frac{2 x - 3}{2} and \frac{2 x - 3}{2} < 4

- 1 \leq \frac{2 x - 3}{2} : x \geq \frac{1}{2}

\frac{2 x - 3}{2} < 4 : x < \frac{11}{2}

Combine the intervals

x \geq \frac{1}{2} and x < \frac{11}{2}

Merge Overlapping Intervals

\frac{1}{2} \leq x < \frac{11}{2}

- 21 x - 6 x^{2}

- 3 ∣ x + 9 ∣ + 2 = 10 ∣ x + 9 ∣ + 5

\frac{- 4 - 5}{8 - 2}

0 = x^{2} - 16 x + 48

(\frac{85}{4})^{\frac{3}{2}}