What is -3/10 < 1/5 x-1/2 < 3/5 ?

The solution to -3/10 < 1/5 x-1/2 < 3/5 is 1<x< 11/2

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-3/10 < 1/5 x-1/2 < 3/5

- \frac{3}{10} < \frac{1}{5} x - \frac{1}{2} < \frac{3}{5}

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

Interval Notation

(1, \frac{11}{2})

Decimal Notation

1 < x < 5.5

Solution steps

- \frac{3}{10} < \frac{1}{5} x - \frac{1}{2} < \frac{3}{5}

a < u < b

then

a < u and u < b

- \frac{3}{10} < \frac{1}{5} x - \frac{1}{2} and \frac{1}{5} x - \frac{1}{2} < \frac{3}{5}

- \frac{3}{10} < \frac{1}{5} x - \frac{1}{2} : x > 1

\frac{1}{5} x - \frac{1}{2} < \frac{3}{5} : x < \frac{11}{2}

Combine the intervals

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

Merge Overlapping Intervals

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

lo g_{8} (2)

x^{2} + 3 \leq 84

5 + 2 d > - 8

∣ x ∣ < - 8

2 + 2 = 5

What is -3/10 < 1/5 x-1/2 < 3/5 ?
The solution to -3/10 < 1/5 x-1/2 < 3/5 is 1<x< 11/2