Alg 2 - Review #2 - Solving Equations and Absolute Values

Front

What is the definition of an 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 inequality |x| < a?

Back

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

Front

What is the solution to the inequality |x| > a?

Back

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

Front

What does the expression |2x + 5| > 11 represent?

Back

It represents the values of x for which the expression 2x + 5 is either greater than 11 or less than -11.

Front

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

Back

You graph an open interval from -a to a, indicating that the endpoints are not included.

Front

What is the first step in solving |2w - 1| < 11?

Back

Split the inequality into two parts: 2w - 1 < 11 and 2w - 1 > -11.

Front

What is the solution to the inequality |2x + 12| < 8?

Back

The solution is -20 < 2x < -4, which simplifies to -10 < x < -2.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values of the variable that satisfy the inequality.

Front

What is the solution to the inequality |x - 3| > 5?

Back

The solution is x < -2 or x > 8.

Front

How do you solve the equation |x + 4| = 7?

Back

Split it into two equations: x + 4 = 7 and x + 4 = -7, leading to x = 3 and x = -11.