Solving and Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you solve the inequality 4x - 2 ≤ -22?

Back

Add 2 to both sides: 4x ≤ -20. Then divide by 4: x ≤ -5.

Front

What is the solution to the inequality 11 > -3y + 2?

Back

Subtract 2 from both sides: 9 > -3y. Then divide by -3 (remember to flip the inequality): y < -3.

Front

How do you solve the inequality 7(x + 3) - 5x < 13?

Back

Distribute: 7x + 21 - 5x < 13. Combine like terms: 2x + 21 < 13. Subtract 21: 2x < -8. Divide by 2: x < -4.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

Distribute: -2x - 4 < 14. Add 4: -2x < 18. Divide by -2 (flip the inequality): x > -9.

Front

Which graph represents the inequality k < 3?

Back

The graph that shows all values to the left of 3, not including 3 itself.

Front

What is the first step in solving an inequality?

Back

Identify the inequality symbol and isolate the variable on one side.

Front

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

Back

The inequality sign flips direction.