Unit 2 Standard#1 Review PAR.4.1 Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥).

Front

What does the symbol '≤' represent in inequalities?

Back

'≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

How do you graph the inequality 5x + y ≤ -1?

Back

To graph 5x + y ≤ -1, first graph the line 5x + y = -1 as a dashed line (since it's ≤, not <). Then shade below the line.

Front

What does 'at most' mean in terms of inequalities?

Back

'At most' translates to the inequality symbol '≤', indicating a maximum limit.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

If y < 2x + 3, what type of line is used to graph this inequality?

Back

A dashed line is used to graph y < 2x + 3, and the area below the line is shaded.

Front

How do you represent Johnny's earnings in an inequality?

Back

If Johnny earns $15 per hour and wants to earn at least $105, the inequality is 15h ≥ 105.

Front

What does the inequality symbol '>' mean?

Back

'>' means 'greater than', indicating that the value on the left is strictly greater than the value on the right.

Front

What is the solution set of the inequality x + 3 < 7?

Back

The solution set is x < 4.

Front

How do you solve the inequality 3x - 5 ≥ 1?

Back

Add 5 to both sides to get 3x ≥ 6, then divide by 3 to find x ≥ 2.