Writing, Graphing, and Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '<' mean?

Back

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

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is greater than 5.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 5 means x is less than or equal to 5.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 5 means x is greater than or equal to 5.

Front

How do you solve the inequality 5z - 2 - 2z < 13?

Back

Combine like terms to get 3z - 2 < 13, then add 2 to both sides: 3z < 15. Finally, divide by 3: z < 5.

Front

What does 'at most' mean in terms of inequalities?

Back

'At most' indicates a maximum limit, represented by the symbol '≤'. For example, if Grace has at most $45, it is written as g ≤ 45.

Front

What does 'at least' mean in terms of inequalities?

Back

'At least' indicates a minimum limit, represented by the symbol '≥'. For example, if there are at least 25 cats, it is written as c ≥ 25.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

How do you solve the inequality 8 - 3k < 8(1 - 7k)?

Back

Distribute on the right: 8 - 3k < 8 - 56k. Add 56k to both sides: 53k < 0. Divide by 53: k < 0.