Solving Inequalities in One Variable

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is larger or smaller than the other.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

How do you solve the inequality 12 ≥ 15 - 6y?

Back

To solve, first isolate y: 12 - 15 ≥ -6y, which simplifies to -3 ≥ -6y. Dividing by -6 flips the inequality: y ≥ ½.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips when you multiply or divide both sides of the inequality by a negative number.

Front

Create an inequality for Jim's pizza budget: He has $8, a slice costs $4, and each topping costs $0.50.

Back

The inequality is 0.50x + 4 ≤ 8, where x is the number of toppings.

Front

When graphing the inequality x < 3, what type of dot is used?

Back

An open dot is used when graphing the inequality x < 3.

Front

Solve the inequality 4x + 3 ≤ -6.

Back

Subtract 3 from both sides: 4x ≤ -9. Then divide by 4: x ≤ -2.25.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

What is the solution set for the inequality y ≥ ½?

Back

The solution set includes all values of y that are greater than or equal to ½.