Final answer:
To solve the inequality 2|2x + 1| < 5, we consider two cases, one where (2x + 1) is positive or zero and one where (2x + 1) is negative. After solving both cases, we combine the results, which leads to the solution -7/4 < x < 3/4.
Step-by-step explanation:
To solve the inequality 2|2x + 1| < 5, we first recognize that the absolute value expression |2x + 1| can take on two possible sets of values: either positive or negative, because the absolute value represents the distance from zero and can never be negative.
1. When (2x + 1) is positive or zero:
2(2x + 1) < 5
4x + 2 < 5
4x < 3
x < 3/4
2. When (2x + 1) is negative:
2(-1)×(2x + 1) < 5
-4x - 2 < 5
-4x < 7
x > -7/4
Combining these two cases, the solution to the inequality is -7/4 < x < 3/4. We can use an inequality symbol to show how these two metric measurements are related, which indicates all the possible values of x that satisfy the original inequality.