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 it mean if |x| = a, where a < 0?

Back

If |x| = a and a is less than 0, there is no solution because absolute values cannot be negative.

Front

Solve for x: |x + 3| = 7.

Back

x = 4 and x = -10.

Front

What is the first step to solve an absolute value equation?

Back

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

Front

Solve for x: |2x - 5| = 3.

Back

x = 4 and x = 1.

Front

What is the solution set for |x| = 0?

Back

The solution set is {0}.

Front

Solve for x: |x - 1| = 5.

Back

x = 6 and x = -4.

Front

What does the equation |x| = a represent graphically?

Back

It represents two points on the number line, a units away from zero, at x = a and x = -a.

Front

Solve for x: |3x + 2| = 8.

Back

x = 2 and x = -rac{10}{3}.

Front

What is the relationship between absolute value and distance?

Back

Absolute value represents the distance of a number from zero on the number line.