What is -1/2+x<3x-2<= 5/2+x ?

The solution to -1/2+x<3x-2<= 5/2+x is 3/4 <x<= 9/4

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-1/2+x<3x-2<= 5/2+x

- \frac{1}{2} + x < 3 x - 2 \leq \frac{5}{2} + x

\frac{3}{4} < x \leq \frac{9}{4}

Interval Notation

(\frac{3}{4}, \frac{9}{4}]

Decimal Notation

0.75 < x \leq 2.25

Solution steps

- \frac{1}{2} + x < 3 x - 2 \leq \frac{5}{2} + x

a < u \leq b

then

a < u and u \leq b

- \frac{1}{2} + x < 3 x - 2 and 3 x - 2 \leq \frac{5}{2} + x

- \frac{1}{2} + x < 3 x - 2 : x > \frac{3}{4}

3 x - 2 \leq \frac{5}{2} + x : x \leq \frac{9}{4}

Combine the intervals

x > \frac{3}{4} and x \leq \frac{9}{4}

Merge Overlapping Intervals

\frac{3}{4} < x \leq \frac{9}{4}

∣ 2 a + 6 ∣ = ∣ 3 a - 6 ∣

11 = \frac{3}{5} (6 x + 10)

x - 12 > 14

x - 3 = 8 x + 3

\frac{5 π}{4} - 2 π

What is -1/2+x<3x-2<= 5/2+x ?
The solution to -1/2+x<3x-2<= 5/2+x is 3/4 <x<= 9/4