Problem 60

Question

Solve each absolute value inequality. $$|x|<5$$

Step-by-Step Solution

Verified
Answer
The solution to the inequality is \( -5 < x < 5 \).
1Step 1: Rewrite as a compound inequality
First, an absolute value inequality \( |x| < 5 \) is equivalent to an inequality -5 < x < 5. This is because the absolute value of a number is the distance of the number from zero on a number line, and all points x within 5 units of zero can be written as -5 < x < 5.
2Step 2: Solve the inequality
The inequality -5 < x < 5 does not require any further steps to solve. The solution is just that x can be any number that is larger than -5 and less than 5.