What is 11x-9<3x+11<7x+13 ?

The solution to 11x-9<3x+11<7x+13 is -1/2 <x< 5/2

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11x-9<3x+11<7x+13

11 x - 9 < 3 x + 11 < 7 x + 13

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

Solution steps

11 x - 9 < 3 x + 11 < 7 x + 13

a < u < b

then

a < u and u < b

11 x - 9 < 3 x + 11 and 3 x + 11 < 7 x + 13

11 x - 9 < 3 x + 11 : x < \frac{5}{2}

3 x + 11 < 7 x + 13 : x > - \frac{1}{2}

Combine the intervals

x < \frac{5}{2} and x > - \frac{1}{2}

Merge Overlapping Intervals

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

- 3 < - 4 x + 1 < 13

1 \leq \frac{( 3 x ^{2} - 7 x + 8 )}{( x ^{2} + 1 )} \leq 2

2 < ∣ x ∣ \leq 5

- x < x^{2} < 6

2 x - 3 < 3 x - 5 < 2 x + 3