Maths-
General
Easy

Question

# Solve each absolute value inequality. Graph the solution :

Hint:

## The correct answer is: Combining the above two solutions, we get -6 < x < 6

### Step by step solution:The given inequality is- 2 >|x| - 8Adding 8 on both sides, we get- 2 + 8 > |x|Finally, we get|x| < 6We use the definition of , which isFor, x < 0,We have Multiplying  on both sides, we haveX > - 6Multiplying  on both sides, we haveX > - 6Or- 6 < xFor, x ≥ 0,We haveThat isX < 6Combining the above two solutions, we get-6 < x < 6We plot the above inequality on the real line.                                          -8        -6        -4        -2         0          2         4         6          8       10The points -6 and 6 are not included in the graph.

The given inequality contains only one variable. So, the graph is plotted on one dimension, which is the real line. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.