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| = b represent?

Back

It represents two possible equations: x - a = b and x - a = -b.

Front

Solve the equation |x - 3| = 0.

Back

x = 3.

Front

What is the solution to the equation |x + 9| = -5?

Back

No solution, because absolute values cannot be negative.

Front

How do you solve the equation |2x - 3| + 5 = 10?

Back

First, isolate the absolute value: |2x - 3| = 5. Then solve 2x - 3 = 5 and 2x - 3 = -5, giving x = 4 and x = -1.

Front

What is the solution to the equation |2x + 9| = 15?

Back

x = 3 and x = -12.

Front

If Sam's house is 14 blocks from the school and Emily lives 6 blocks from Sam, how do you express Emily's distance from the school using an absolute value equation?

Back

|x - 14| = 6.

Front

What is the general form of an absolute value equation?

Back

The general form is |A| = B, where A is an expression and B is a non-negative number.

Front

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

Back

It means that the equation cannot be satisfied by any real number, often because the absolute value is set equal to a negative number.

Front

How do you graph an absolute value function?

Back

The graph of an absolute value function forms a V shape, opening upwards if the coefficient of x is positive.