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 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the inequality 15 + 7x ≥ 29?

Back

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

Front

What is the solution to the inequality 4x - 10 ≤ 22?

Back

Add 10 to both sides: 4x ≤ 32. Then divide by 4: x ≤ 8.

Front

When do you flip the inequality sign?

Back

You flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

Solve the inequality -3x + 2 ≤ 22.

Back

Subtract 2 from both sides: -3x ≤ 20. Then divide by -3 (flip the sign): x ≥ -20/3.

Front

What is the solution to the inequality 4x - 3 < -1x + 12?

Back

Combine like terms: 5x < 15. Then divide by 5: x < 3.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality means to represent the solution set on a number line, using an open circle for < or > and a closed circle for ≤ or ≥.

Front

What is the difference between 'x < 5' and 'x ≤ 5'?

Back

'x < 5' means x can be any number less than 5, while 'x ≤ 5' means x can be 5 or any number less than 5.