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'. For example, x > 5 means x is greater than 5.

Front

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

Back

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

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is greater than or equal to 4.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 7 means x is less than or equal to 7.

Front

How do you solve the inequality 15 > x - 1?

Back

Add 1 to both sides: 16 > x, or x < 16.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities using 'and' or 'or'. For example, x < 5 or x > 10.

Front

How do you represent the situation: 'Your family needs 2 gallons of water this week, but you don’t want to buy any more than 8 gallons'?

Back

The inequality is 2 ≤ x ≤ 8.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

First, subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the solution to the inequality 10 ≥ x - 3?

Back

Add 3 to both sides: 13 ≥ x, or x ≤ 13.