Solving 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'. 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'. 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 or equal to'. It indicates that the value on the left is either larger than or equal to 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

How do you solve the inequality 84 - 4x ≤ 52?

Back

First, subtract 84 from both sides: -4x ≤ -32. Then, divide by -4 (remember to flip the inequality): x ≥ 8.

Front

What is the solution to the inequality 10 - 3x < 16?

Back

Subtract 10 from both sides: -3x < 6. Then, divide by -3 (flip the inequality): x > -2.

Front

When graphing the inequality 2x + 3 < 7, what type of circle is used?

Back

An open circle is used for '<' to indicate that the endpoint is not included in the solution.

Front

What is the solution to the inequality 28 + 2x > 50?

Back

Subtract 28 from both sides: 2x > 22. Then, divide by 2: x > 11.

Front

What is the difference between an open circle and a closed circle on a number line?

Back

An open circle indicates that the number is not included in the solution (for < or >), while a closed circle indicates that the number is included (for ≤ or ≥).