LT 4b Inequalities

Front

What is an AND compound inequality?

Back

An AND compound inequality is a statement that combines two inequalities and is true only when both inequalities are true simultaneously.

Front

What is an OR compound inequality?

Back

An OR compound inequality is a statement that combines two inequalities and is true if at least one of the inequalities is true.

Front

What is the first step to solve |2x + 12| < 8?

Back

The first step is to split it into two inequalities: 2x + 12 < 8 and 2x + 12 > -8.

Front

How do you solve the inequality 6 - 2|m - 3| > -4?

Back

First, isolate the absolute value: 6 + 4 > 2|m - 3|, then simplify to 10 > 2|m - 3|.

Front

What does the absolute value represent in inequalities?

Back

The absolute value represents the distance from zero on the number line, which can lead to two possible cases in inequalities.

Front

What is the solution set for the inequality |x - 5| < 3?

Back

The solution set is 2 < x < 8.

Front

How do you graph the solution to an absolute value inequality?

Back

You graph the critical points found from the inequality and shade the region that satisfies the inequality.

Front

What is the first step in solving |x + 4| > 7?

Back

Split into two inequalities: x + 4 > 7 or x + 4 < -7.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that satisfy the inequality, often occurring when the inequalities contradict each other.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) do include them.