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?

Back

The symbol '>' means 'greater than'. For example, 6 > 4 means 6 is greater than 4.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. For example, 3 < 5 means 3 is less than 5.

Front

How do you solve the inequality 7b - 3 < 11?

Back

Add 3 to both sides: 7b < 14. Then divide by 7: b < 2.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

Distribute -2: -2x - 4 < 14. Add 4 to both sides: -2x < 18. Divide by -2 (reverse the inequality): x > -9.

Front

How do you isolate x in the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then subtract 10: x > -22.

Front

What is the solution to the inequality 11x + 16 < 43 + 2x?

Back

Subtract 2x from both sides: 9x + 16 < 43. Then subtract 16: 9x < 27. Divide by 9: x < 3.

Front

What does it mean to reverse the inequality sign?

Back

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

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, such as a < x < b, meaning x is between a and b.

Front

How do you graph the inequality x < 3?

Back

Draw a number line, place an open circle at 3, and shade to the left to indicate all numbers less than 3.