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

The solution to 3<= (-2x+3)/2 <4 is -5/2 <x<=-3/2

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

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

- \frac{5}{2} < x \leq - \frac{3}{2}

Interval Notation

(- \frac{5}{2}, - \frac{3}{2}]

Decimal Notation

- 2.5 < x \leq - 1.5

Solution steps

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

a \leq u < b

then

a \leq u and u < b

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

3 \leq \frac{- 2 x + 3}{2} : x \leq - \frac{3}{2}

\frac{- 2 x + 3}{2} < 4 : x > - \frac{5}{2}

Combine the intervals

x \leq - \frac{3}{2} and x > - \frac{5}{2}

Merge Overlapping Intervals

- \frac{5}{2} < x \leq - \frac{3}{2}

12 x^{2} + 7 x + 1 = 0

x^{2} - 18 x + 68 = 0

5 x - 7 = - 22

2 - \frac{4}{9}

7 x - x^{2} = 10