Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve the inequality |x| < a?

Back

To solve |x| < a, you split it into two inequalities: -a < x < a.

Front

How do you solve the inequality |x| > a?

Back

To solve |x| > a, you split it into two inequalities: x < -a or x > a.

Front

What does the solution |y - 1| ≤ 6 represent on a number line?

Back

The solution -5 ≤ y ≤ 7 represents all the values of y that are within 6 units of 1 on the number line.

Front

What does the solution |p + 3| ≥ 10 indicate about p?

Back

The solution p ≤ -13 or p ≥ 7 indicates that p is either less than or equal to -13 or greater than or equal to 7.

Front

What is the first step in solving an absolute value equation?

Back

The first step is to isolate the absolute value expression on one side of the equation.

Front

What is the difference between |x| < a and |x| ≤ a?

Back

|x| < a means x is strictly within a units from zero, while |x| ≤ a includes the endpoints, meaning x can be exactly a units from zero.

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What is the difference between |x| > a and |x| ≥ a?

Back

|x| > a means x is strictly outside a units from zero, while |x| ≥ a includes the endpoints, meaning x can be exactly a units from zero.

Front

How do you graph the solution of |x| < a?

Back

You graph the interval (-a, a) on the number line, using open circles to indicate that the endpoints are not included.

Front

How do you graph the solution of |x| > a?

Back

You graph the regions x < -a and x > a on the number line, using open circles to indicate that the endpoints are not included.