Algebra 1: Unit 1 Assessment (Solving Equations & Inequalities)

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities, typically using 'and' or 'or'. For example, x > 2 and x < 5.

Front

What does the inequality |x| > 3 represent?

Back

The inequality |x| > 3 means that x is either greater than 3 or less than -3, represented as x > 3 or x < -3.

Front

How do you solve the equation |x - 3| = 7?

Back

To solve |x - 3| = 7, set up two equations: x - 3 = 7 and x - 3 = -7. The solutions are x = 10 and x = -4.

Front

What does the inequality 2 < x ≤ 6 mean?

Back

The inequality 2 < x ≤ 6 means that x is greater than 2 and less than or equal to 6.

Front

How do you solve the inequality 2x - 3 > 7?

Back

To solve 2x - 3 > 7, add 3 to both sides to get 2x > 10, then divide by 2 to find x > 5.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

In compound inequalities, 'and' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.

Front

What is the solution set for the inequality x < 5?

Back

The solution set for x < 5 includes all real numbers less than 5.

Front

How do you graph the inequality x > 3?

Back

To graph x > 3, draw a number line, place an open circle at 3, and shade to the right to indicate all numbers greater than 3.

Front

What does the absolute value |x| represent?

Back

The absolute value |x| represents the distance of x from 0 on the number line, regardless of direction.

Front

What is the solution to the inequality x + 4 < 10?

Back

To solve x + 4 < 10, subtract 4 from both sides to find x < 6.