1.4 Solving Absolute Value Equations

Front

What is an 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

What does the equation |x| = a imply?

Back

It implies that x = a or x = -a, where a is a non-negative number.

Front

Is |x + 5| = -9 possible?

Back

No, because absolute values cannot be negative.

Front

What are the solutions to the equation |2a - 10| = 6?

Back

The solutions are a = 8 and a = 2.

Front

How do you express |d + 3| = 6 - 2d in two separate equations?

Back

You can express it as d + 3 = 6 - 2d and d + 3 = -(6 - 2d).

Front

What is the first step in solving |-2 - 4n| = 34?

Back

Set up two equations: -2 - 4n = 34 and -2 - 4n = -34.

Front

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

Back

It means that there are no values for the variable that can satisfy the equation.

Front

How do you determine the order of numbers involving absolute values?

Back

Calculate the absolute values and then compare the results to order the numbers.

Front

What is the solution set for |x - 1| = 3?

Back

The solution set is x = 4 and x = -2.