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

How do you solve an absolute value equation of the form |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What is the solution to the equation |x - 5| = 3?

Back

x = 8 or x = 2.

Front

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

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal the given value (e.g., |x| = -3 has no solution).

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, you perform algebraic operations to get the absolute value expression by itself on one side of the equation.

Front

What is the solution to the equation |2x + 1| = 5?

Back

x = 2 or x = -3.

Front

How do you graph an absolute value function?

Back

An absolute value function is V-shaped, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

What is the general form of an absolute value equation?

Back

The general form is |ax + b| = c, where a, b, and c are constants.

Front

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

Back

x = -2 or x = -6.

Front

How do you check your solution for an absolute value equation?

Back

Substitute the solution back into the original equation to see if both sides are equal.