How Do You Know If an Absolute Value Inequality Is All Real Numbers

Absolute Value Inequalities. Here are the steps to follow when solving absolute value inequalities: Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.

How do you know if the answer is all real numbers?

Combine like terms on both sides of the equation. Isolate the x term by subtracting x from both sides. You arrive at the true statement “3 = 3”. When you end up with a true statement like this, it means that the solution to the equation is “all real numbers”.

Is absolute value function all real numbers?

Absolute value can be expressed as a function: f(x) = |x| = x if x is positive, = -x if x is negative. The domain includes all real numbers (absolute value can be expanded to more numbers once we introduce them), and the range is all non-negative numbers (all positive numbers and 0).