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Popular >

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

Solution

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

Solution

x \geq \frac{16}{3}

+2

Interval Notation

[\frac{16}{3}, \infty)

Decimal Notation

x \geq 5.33333 \dots

Solution steps

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

If

a \leq u \leq b

then

a \leq u and u \leq b

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

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

\frac{5}{2} x + 2 \leq 3 x - \frac{2}{3} : x \geq \frac{16}{3}

Combine the intervals

x \geq - 1 and x \geq \frac{16}{3}

Merge Overlapping Intervals

x \geq \frac{16}{3}

Popular Examples

\frac{q}{2} < 2

2(1+5x)=5(2x-1)

2 (1 + 5 x) = 5 (2 x - 1)

simplify 3/(-2)simplify

\frac{3}{- 2}

|x^2-1|+|x^2-16|>= 2

x^{2} - 1 + x^{2} - 16 \geq 2

- 3 w - 4 = w + 3

Frequently Asked Questions (FAQ)

What is 3/2 x+1<= 5/2 x+2<= 3x-2/3 ?
The solution to 3/2 x+1<= 5/2 x+2<= 3x-2/3 is x>= 16/3