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 in an inequality?

Back

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

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller than or equal to the value on the right.

Front

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

Back

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

Front

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

Back

First, simplify: 7x + 21 - 5x < 13. Then, combine like terms: 2x + 21 < 13. Subtract 21 from both sides: 2x < -8. Finally, divide by 2: x < -4.

Front

How do you solve the inequality 6(n + 2) < -72?

Back

First, simplify: 6n + 12 < -72. Then, subtract 12 from both sides: 6n < -84. Finally, divide by 6: n < -14.

Front

How do you solve the inequality 8x ≥ -32?

Back

Divide both sides by 8: x ≥ -4.

Front

How do you solve the inequality 3(x - 2) - 2x < 18?

Back

First, simplify: 3x - 6 - 2x < 18. Then, combine like terms: x - 6 < 18. Add 6 to both sides: x < 24.

Front

What is the solution to the inequality x < -4?

Back

The solution indicates that x can be any number less than -4.