Question

Why do we write 2 inequalities when we have an absolute value to solve?

A. One inequality represents the positive solution, and the other represents the negative solution.

B. Two inequalities ensure that all possible solutions, both positive and negative, are considered.

C. Writing 2 inequalities is a common mathematical practice with no specific reason.

D. One inequality represents the exact solution, and the other represents an approximation of the solution.

Answer 1

When solving an absolute value equation, we write two inequalities to account for both the positive and negative solutions.

Step-by-step explanation:

When solving an absolute value equation, we write two inequalities to account for both the positive and negative solutions. This is because the absolute value of a number is the distance from that number to zero on a number line, and that distance can be positive or negative.

For example, let's say we have the equation |x| = 3. We can write two separate inequalities: x = 3 and x = -3. By solving both inequalities, we find that x can be either 3 or -3, which are the two solutions to the absolute value equation.