Solving Absolute Value Equations (2.14.2)

Question 1

• The absolute value of a number states how far that number lies on the number line from 0. It does not indicate in which direction the number lies; i.e., whether it is positive or negative.

Answer 1

• The absolute value of a number states how far that number lies on the number line from 0. It does not indicate in which direction the number lies; i.e., whether it is positive or negative.

Question 2

• The notation for absolute value places a vertical line on each side of the variable, number or expression for which absolute value is denoted; e.g., |x| indicates “absolute value of x.”

Answer 2

• The notation for absolute value places a vertical line on each side of the variable, number or expression for which absolute value is denoted; e.g., |x| indicates “absolute value of x.”

Question 3

• If the absolute value of a number is equal to a value, you know that the number lies that many units from 0 in one direction or the other.

Answer 3

• If the absolute value of a number is equal to a value, you know that the number lies that many units from 0 in one direction or the other.

Question 4

The absolute value in this case indicates that the expression (3x – 1) equals +2 or –2. You must solve for both.

Set up the equations for each possibility.
Solve for x in each equation.

Answer 4

The absolute value in this case indicates that the expression (3x – 1) equals +2 or –2. You must solve for both.

Set up the equations for each possibility.
Solve for x in each equation.

Question 5

When you substitute each of these values into the expression, you find that both work. When x = 1, your expression is |2| which is 2. When x = –1/3, your expression is |–2| which is also 2.

Answer 5

When you substitute each of these values into the expression, you find that both work. When x = 1, your expression is |2| which is 2. When x = –1/3, your expression is |–2| which is also 2.

Question 6

The process is the same with this example. However, you
will have additional steps because of the rational expression.

Set up both equations.

Cross multiply to eliminate the denominators.

Solve for x.

Remember to check your answers.

Answer 6

The process is the same with this example. However, you
will have additional steps because of the rational expression.

Set up both equations.

Cross multiply to eliminate the denominators.

Solve for x.

Remember to check your answers.