What is -0.1+11<sqrt(18x+31)-11+11<0.1+11 ?

The solution to -0.1+11<sqrt(18x+31)-11+11<0.1+11 is 4.87833…<x<5.12277…

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-0.1+11<sqrt(18x+31)-11+11<0.1+11

- 0.1 + 11 < 18 x + 31 - 11 + 11 < 0.1 + 11

4.87833 \dots < x < 5.12277 \dots

Solution steps

- 0.1 + 11 < 18 x + 31 - 11 + 11 < 0.1 + 11

a < u < b

then

a < u and u < b

- 0.1 + 11 < 18 x + 31 - 11 + 11 and 18 x + 31 - 11 + 11 < 0.1 + 11

- 0.1 + 11 < 18 x + 31 - 11 + 11 : x > 4.87833 \dots

18 x + 31 - 11 + 11 < 0.1 + 11 : - \frac{31}{18} \leq x < 5.12277 \dots

Combine the intervals

x > 4.87833 \dots and - \frac{31}{18} \leq x < 5.12277 \dots

Merge Overlapping Intervals

4.87833 \dots < x < 5.12277 \dots

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What is -0.1+11<sqrt(18x+31)-11+11<0.1+11 ?
The solution to -0.1+11<sqrt(18x+31)-11+11<0.1+11 is 4.87833…<x<5.12277…