Absolute Value Inequality

Solve the inequality:  |2x - 1| < 7

Absolute value is the distance away from zero.

|2x - 1| < 7   {the distance (2x - 1) is from zero, is less than 7}

The two numbers that are 7 away from zero are 7 and -7.  Therefore, (2x - 1) is between 7 and -7.

-7 < 2x - 1 < 7   {the value of (2x - 1) lies between 7 and -7}
+1         +1   +1
-6 < 2x < 8   {added 1 to the left, the middle, and the right}
-3 < x < 4   {divided the left, middle, and right by 2}

- Algebra House