SOLUTION: |sqrt(x+3)-((7+x)/4)|<0.5 How to solve this inequality? I get -2.07<x<1.9 But according to the textbook, it is -2.6<x<8.6 Please help Thank you

Question 1206574: |sqrt(x+3)-((7+x)/4)|<0.5
How to solve this inequality? I get -2.07 But according to the textbook, it is -2.6 Please help
Thank you
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

and

It turns out that the maximum value of is 0, so we only need to solve the inequality . If you try to solve the inequality you will find that there are no real solutions.

Solve the corresponding EQUATION to find the endpoints of the solution interval.

Multiply everything by 4 to clear fractions

Isolate the term with the radical

Square both sides to eliminate the radical

The quadratic does not factor; use the quadratic formula
or
or
or

To 3 decimal places, the solutions are -2.657 and 8.657.

A graph....

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