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

The solution to 1/2 <= (x+1)/3 < 3/4 is 1/2 <= x< 5/4

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

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

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

Solution steps

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

a \leq u < b

then

a \leq u and u < b

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

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

\frac{x + 1}{3} < \frac{3}{4} : x < \frac{5}{4}

Combine the intervals

x \geq \frac{1}{2} and x < \frac{5}{4}

Merge Overlapping Intervals

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

- 8 x + 1 = - 8 x + 2

3.2 = - 0.4 nn

x^{4} + 5 x^{2} + 6

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

What is 1/2 <= (x+1)/3 < 3/4 ?
The solution to 1/2 <= (x+1)/3 < 3/4 is 1/2 <= x< 5/4