Two-Variable Inequalities

Front

What is a two-variable inequality?

Back

An inequality that involves two variables, typically expressed in the form of ax + by <, >, ≤, or ≥ c.

Front

What does the symbol '>' mean in an inequality?

Back

It means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' mean in an inequality?

Back

It means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What does the symbol '≥' mean in an inequality?

Back

It means 'greater than or equal to'. For example, x ≥ 4 means x is any number greater than or equal to 4.

Front

What does the symbol '≤' mean in an inequality?

Back

It means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

How do you graph a two-variable inequality?

Back

1. Graph the corresponding equation as a line. 2. Use a dashed line for < or >, and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What happens to the inequality symbol when you multiply or divide both sides by a negative number?

Back

The inequality symbol flips. For example, if -2x > 6, dividing by -2 gives x < -3.

Front

Write an inequality for the following situation: A store sells apples for $2 each and oranges for $3 each. If you want to spend at most $20, what is the inequality?

Back

2a + 3o ≤ 20, where a = number of apples and o = number of oranges.

Front

What is the solution set of the inequality 3x - 5 < 4?

Back

x < 3.

Front

How do you solve the inequality 5y + 2 ≥ 17?

Back

Subtract 2 from both sides: 5y ≥ 15. Then divide by 5: y ≥ 3.