Solving Absolute Value Inequalities (2.14.4)

Question 1

• Absolute values within inequalities are best discerned using a number line graph. Sketch one out for each problem so you
can visually study the possibilities.

Answer 1

• Absolute values within inequalities are best discerned using a number line graph. Sketch one out for each problem so you
can visually study the possibilities.

Question 2

• If the absolute value is less than the value stated, your absolute value expression will be greater than the negative value
and smaller than the positive value stated; i.e., |A|

Answer 2

• If the absolute value is less than the value stated, your absolute value expression will be greater than the negative value
and smaller than the positive value stated; i.e., |A|

Question 3

• If the absolute value is greater than the value stated, your absolute value expression will be smaller than the negative value
and larger than the positive value stated; i.e., |A| > B means A B. The expression’s value is outside the
boundaries set by the positive and negative values of the inequality

Answer 3

• If the absolute value is greater than the value stated, your absolute value expression will be smaller than the negative value
and larger than the positive value stated; i.e., |A| > B means A B. The expression’s value is outside the
boundaries set by the positive and negative values of the inequality

Question 4

Because the absolute value is greater than or equal to the
stated value of 7, its solutions lie outside the boundaries set
at –7 and +7.
This fact creates the two equations to solve.

Answer 4

Because the absolute value is greater than or equal to the
stated value of 7, its solutions lie outside the boundaries set
at –7 and +7.
This fact creates the two equations to solve.

Question 5

Solve the two equations.
Remember to check your answers to be sure they work in the
original equation.

Answer 5

Solve the two equations.
Remember to check your answers to be sure they work in the
original equation.

Question 6

In a “less than” inequality, all the possible solutions for the
absolute value expression |6x + 4| will lie within the
boundaries set at –1 and +1.
This sets up your two equations. Notice that in this problem
you’ve used an alternate notation showing two relationships
within one sentence. This is sometimes used to save writing.
Be sure your thinking stays accurate as you work towards
your solutions.
Remember to check your answers.

Answer 6

In a “less than” inequality, all the possible solutions for the
absolute value expression |6x + 4| will lie within the
boundaries set at –1 and +1.
This sets up your two equations. Notice that in this problem
you’ve used an alternate notation showing two relationships
within one sentence. This is sometimes used to save writing.
Be sure your thinking stays accurate as you work towards
your solutions.
Remember to check your answers.