Absolute Value Equations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What does the equation |x| = a represent?

Back

It represents two possible equations: x = a and x = -a, where a is a non-negative number.

Front

What is the solution to the equation |x| = 0?

Back

The solution is x = 0.

Front

How do you solve the equation |x - 3| = 5?

Back

Set up two equations: x - 3 = 5 and x - 3 = -5. The solutions are x = 8 and x = -2.

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression on one side of the equation.

Front

What does it mean if an absolute value equation has no solution?

Back

It means that the expression inside the absolute value cannot equal the value on the other side of the equation.

Front

Solve for x: |2x + 1| = 7

Back

x = 3 and x = -4.

Front

What is the solution to the equation |x + 4| + 2 = 0?

Back

No Solution, because the absolute value cannot be negative.

Front

How do you interpret the equation |x| + b = c?

Back

Isolate |x| to find |x| = c - b, then solve for x.

Front

What is the solution to the equation |x - 2| = 3?

Back

x = 5 and x = -1.