Absolute Value Equations and Inequalities

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

How do you solve the equation |x| = a where a > 0?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What is the solution set for the equation |x| = 24?

Back

The solution set is {24, -24}.

Front

How do you solve the equation |2a - 10| = 6?

Back

Set up two equations: 2a - 10 = 6 and 2a - 10 = -6. Solve each for a to get a = 8 and a = 2.

Front

What does the compound inequality involving 'or' signify in absolute value inequalities?

Back

It signifies that the solutions are found in two separate intervals.

Front

What does the compound inequality involving 'and' signify in absolute value inequalities?

Back

It signifies that the solutions must satisfy both conditions simultaneously.

Front

How do you express the solution to the inequality |x| < a?

Back

The solution is expressed as -a < x < a.

Front

How do you express the solution to the inequality |x| > a?

Back

The solution is expressed as x < -a or x > a.

Front

What is the graphical representation of |x| < a?

Back

It is represented by an open interval on the number line between -a and a.

Front

What is the graphical representation of |x| > a?

Back

It is represented by two separate intervals on the number line, one to the left of -a and one to the right of a.