What is 1/2 <(3x+7)/2 <= 4 ?

The solution to 1/2 <(3x+7)/2 <= 4 is -2<x<= 1/3

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1/2 <(3x+7)/2 <= 4

\frac{1}{2} < \frac{3 x + 7}{2} \leq 4

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

Interval Notation

(- 2, \frac{1}{3}]

Decimal Notation

- 2 < x \leq 0.33333 \dots

Solution steps

\frac{1}{2} < \frac{3 x + 7}{2} \leq 4

a < u \leq b

then

a < u and u \leq b

\frac{1}{2} < \frac{3 x + 7}{2} and \frac{3 x + 7}{2} \leq 4

\frac{1}{2} < \frac{3 x + 7}{2} : x > - 2

\frac{3 x + 7}{2} \leq 4 : x \leq \frac{1}{3}

Combine the intervals

x > - 2 and x \leq \frac{1}{3}

Merge Overlapping Intervals

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

3 x^{2} y - 9 x^{3} y^{3}

- 5 - 9

25 p^{2} - 9

6 - (3 x + 10) + 4 (2 - x) = 15

1 - \frac{2 x + 5}{7} = - x + \frac{3 - x}{2}