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

Algebra ->  Absolute-value -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!


abs%28sqrt%28x%2B3%29-%287%2Bx%29%2F4%29%3C0.5

-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5

-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4 and sqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5

It turns out that the maximum value of sqrt%28x%2B3%29-%287%2Bx%29%2F4 is 0, so we only need to solve the inequality -0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0. If you try to solve the inequality sqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5 you will find that there are no real solutions.

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

-0.5=sqrt%28x%2B3%29-%287%2Bx%29%2F4

Multiply everything by 4 to clear fractions
-2=4sqrt%28x%2B3%29-7-x

Isolate the term with the radical
x%2B5=4sqrt%28x%2B3%29

Square both sides to eliminate the radical
x%5E2%2B10x%2B25=16x%2B48
x%5E2-6x-23=0

The quadratic does not factor; use the quadratic formula
x=%286%2Bsqrt%2836%2B92%29%29%2F2 or x=%286-sqrt%2836%2B92%29%29%2F2
x=%286%2B8sqrt%282%29%29%2F2 or x=%286-8sqrt%282%29%29%2F2
x=3%2B4sqrt%282%29 or x=3-4sqrt%282%29

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

A graph....