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}
|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
