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 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

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

Back

The symbol '<' means 'less than'. For example, x < 5 means x is any number less than 5.

Front

How do you solve the inequality -7 + 10z > -27?

Back

Add 7 to both sides: 10z > -20. Then divide by 10: z > -2.

Front

What is the solution to the inequality -9a - 1 < 26?

Back

Add 1 to both sides: -9a < 27. Then divide by -9 (remember to flip the inequality): a > -3.

Front

Which graph represents the inequality -2 ≥ n?

Back

The graph should show a closed circle at -2 and a line extending to the left.

Front

How do you solve the inequality 5y - 11 ≥ 9?

Back

Add 11 to both sides: 5y ≥ 20. Then divide by 5: y ≥ 4.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is any number greater than or equal to 2.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is any number less than or equal to 4.

Front

How do you graph the solution to the inequality 11x + 14 < -8?

Back

First, solve for x: 11x < -22, then x < -2. The graph should show an open circle at -2 and a line extending to the left.