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?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you solve the inequality -3 + x ≤ -11?

Back

Add 3 to both sides: x ≤ -8.

Front

How do you solve the inequality 6x - 4 ≥ 26?

Back

Add 4 to both sides: 6x ≥ 30. Then divide by 6: x ≥ 5.

Front

How do you solve the inequality 0.5(x - 8) < 2?

Back

Multiply both sides by 2: x - 8 < 4. Then add 8: x < 12.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality means representing the solutions of the inequality on a number line, using an open or closed circle to indicate whether the endpoint is included.

Front

What is the difference between 'x < -2' and 'x ≤ -2'?

Back

'x < -2' means x is less than -2 (not including -2), while 'x ≤ -2' means x is less than or equal to -2 (including -2).

Front

Translate: 5 times a number is at least 60.

Back

5x ≥ 60.

Front

What is the solution set for the inequality x < -2?

Back

The solution set includes all numbers less than -2.