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?

Back

To solve an absolute value equation, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

Solve for x: |x| = a (where a > 0)

Back

x = a or x = -a.

Front

What is the solution to |x| = 0?

Back

The solution is x = 0.

Front

Solve for x: |x - 3| = 5

Back

x = 8 or x = -2.

Front

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

Back

It means that there are no values of x that can satisfy the equation, often because the absolute value cannot equal a negative number.

Front

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

Back

x = 3 or x = -4.

Front

What is the first step in solving |4x - 3| = 17?

Back

Set up two equations: 4x - 3 = 17 and 4x - 3 = -17.

Front

Solve for x: |−2n| + 10 = −50

Back

No Solution.

Front

What is the solution to |3x - 6| - 9 = -3?

Back

x = 0 or x = 4.