What is -6.5<= (7x+6)/2 <= 20.5 ?

The solution to -6.5<= (7x+6)/2 <= 20.5 is -19/7 <= x<= 5

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-6.5<= (7x+6)/2 <= 20.5

- 6.5 \leq \frac{7 x + 6}{2} \leq 20.5

- \frac{19}{7} \leq x \leq 5

Interval Notation

[- \frac{19}{7}, 5]

Decimal Notation

- 2.71428 \dots \leq x \leq 5

Solution steps

- 6.5 \leq \frac{7 x + 6}{2} \leq 20.5

a \leq u \leq b

then

a \leq u and u \leq b

- 6.5 \leq \frac{7 x + 6}{2} and \frac{7 x + 6}{2} \leq 20.5

- 6.5 \leq \frac{7 x + 6}{2} : x \geq - \frac{19}{7}

\frac{7 x + 6}{2} \leq 20.5 : x \leq 5

Combine the intervals

x \geq - \frac{19}{7} and x \leq 5

Merge Overlapping Intervals

- \frac{19}{7} \leq x \leq 5

0 = 3 x^{2} + 1

9 + 3 x > 12

5 x^{2} - 30 x - 135 = 0

12 = 2 (6 x - 6)

- 3 \leq \frac{4 x + 17}{2} < 5

What is -6.5<= (7x+6)/2 <= 20.5 ?
The solution to -6.5<= (7x+6)/2 <= 20.5 is -19/7 <= x<= 5