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

The solution to 3/4 x-2<= 2x+1<= 1/4 x+2 is -12/5 <= x<= 4/7

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3/4 x-2<= 2x+1<= 1/4 x+2

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

- \frac{12}{5} \leq x \leq \frac{4}{7}

Interval Notation

[- \frac{12}{5}, \frac{4}{7}]

Decimal Notation

- 2.4 \leq x \leq 0.57142 \dots

Solution steps

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

a \leq u \leq b

then

a \leq u and u \leq b

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

\frac{3}{4} x - 2 \leq 2 x + 1 : x \geq - \frac{12}{5}

2 x + 1 \leq \frac{1}{4} x + 2 : x \leq \frac{4}{7}

Combine the intervals

x \geq - \frac{12}{5} and x \leq \frac{4}{7}

Merge Overlapping Intervals

- \frac{12}{5} \leq x \leq \frac{4}{7}

∣ 2 x + 4 ∣ = 16

v^{2} = 54 - 12 v

\frac{3}{7} x + 5 = 8

36 g^{2} - 49 h^{2}

x^{2} - x - 20 \leq 0

What is 3/4 x-2<= 2x+1<= 1/4 x+2 ?
The solution to 3/4 x-2<= 2x+1<= 1/4 x+2 is -12/5 <= x<= 4/7