Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is not equal to the other.

Front

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

Back

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

Front

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

Back

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

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 side is either larger than or equal to the value on the right side.

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 side is either smaller than or equal to the value on the right side.

Front

How do you solve the inequality 4x + 6 > 22?

Back

Subtract 6 from both sides: 4x > 16. Then divide by 4: x > 4.

Front

Translate: 3 times a number is less than 15.

Back

3x < 15.

Front

How do you solve the inequality -9x + 7 ≥ 25?

Back

Subtract 7 from both sides: -9x ≥ 18. Then divide by -9 (remember to flip the inequality): x ≤ -2.

Front

What is the solution to the inequality 15 + 7x ≥ 29?

Back

Subtract 15 from both sides: 7x ≥ 14. Then divide by 7: x ≥ 2.

Front

How do you represent the inequality x < 2 on a number line?

Back

Draw a number line and place an open circle at 2, shading to the left to indicate all numbers less than 2.