Ch 8 TEST Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is an equation 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 equation |x| = a?

Back

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

Front

What does the equation |5x| = 40 represent?

Back

It represents two equations: 5x = 40 and 5x = -40, leading to solutions x = 8 and x = -8.

Front

What is the solution set for |2x - 1| = 9?

Back

The solution set is x = 5 and x = -4.

Front

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

Back

The inequality |x| < a means that x is between -a and a, or -a < x < a.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' (conjunction) or 'or' (disjunction).

Front

What does the inequality |4k + 12| ≥ 6 mean?

Back

It means that 4k + 12 is either greater than or equal to 6 or less than or equal to -6.

Front

How do you solve the inequality |x - 3| < 5?

Back

You set up the compound inequality: -5 < x - 3 < 5, which simplifies to -2 < x < 8.

Front

What is the solution to the equation |2a - 10| = 6?

Back

The solutions are a = 8 and a = 2.

Front

What is the difference between conjunction and disjunction in inequalities?

Back

Conjunction requires both conditions to be true (AND), while disjunction requires at least one condition to be true (OR).