## dorin2 2 years ago Solve the inequality |x-3|<2

1. samsterz

1<x<5 that sound right?

2. samsterz

It's 1<x<5

3. samsterz

@dorin2

4. dorin2

5. samsterz

want me to explain it, is that what ur asking?

6. samsterz

im 99.99% sure its right nearly , the only mistake that there could possibly be is that somehow i cant see the problem correctly

7. samsterz

|x−3|<2 Remove the absolute value term. This creates a ± on the right-hand side of the equation because |x|=±x. x−3<±(2) Set up the + portion of the ± solution. x−3<2 Move all terms not containing x to the right-hand side of the inequality. x<5 Set up the − portion of the ± solution. When solving the − portion of an inequality, flip the direction of the inequality sign. x−3>−(2) Multiply −1 by the 2 inside the parentheses. x−3>−2 Since −3 does not contain the variable to solve for, move it to the right-hand side of the inequality by adding 3 to both sides. x>3−2 Subtract 2 from 3 to get 1. x>1 The solution to the inequality includes both the positive and negative versions of the absolute value. x<5 and x>1 The solution is the set of values where x<5andx>1. 1<x<5

8. samsterz

Thats how u solve it, ur welcome

9. dorin2

Thank you.....