What is 2/3 x-2<2x-3<6+2/3 x ?

The solution to 2/3 x-2<2x-3<6+2/3 x is 3/4 <x< 27/4

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2/3 x-2<2x-3<6+2/3 x

\frac{2}{3} x - 2 < 2 x - 3 < 6 + \frac{2}{3} x

\frac{3}{4} < x < \frac{27}{4}

Interval Notation

(\frac{3}{4}, \frac{27}{4})

Decimal Notation

0.75 < x < 6.75

Solution steps

\frac{2}{3} x - 2 < 2 x - 3 < 6 + \frac{2}{3} x

a < u < b

then

a < u and u < b

\frac{2}{3} x - 2 < 2 x - 3 and 2 x - 3 < 6 + \frac{2}{3} x

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

2 x - 3 < 6 + \frac{2}{3} x : x < \frac{27}{4}

Combine the intervals

x > \frac{3}{4} and x < \frac{27}{4}

Merge Overlapping Intervals

\frac{3}{4} < x < \frac{27}{4}

\frac{x}{9} + \frac{1}{3} = \frac{1}{18}

(x + 1)^{2} - 20 = (x - 3)^{2}

0 = - 3 x + 6

\frac{5 b}{6 a} + \frac{3 b}{10 a ^{2}} + \frac{2}{a b ^{2}}

lo g_{25} (5)

What is 2/3 x-2<2x-3<6+2/3 x ?
The solution to 2/3 x-2<2x-3<6+2/3 x is 3/4 <x< 27/4