Inequality Test

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' mean in inequalities?

Back

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

Front

What does the symbol '≥' mean in inequalities?

Back

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

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

How do you solve the inequality -3x + 1 ≤ 13?

Back

To solve -3x + 1 ≤ 13, subtract 1 from both sides to get -3x ≤ 12, then divide by -3 (remember to flip the inequality sign) to get x ≥ -4.

Front

What is the solution to the inequality 3(x - 1) ≥ -9?

Back

To solve 3(x - 1) ≥ -9, first distribute to get 3x - 3 ≥ -9. Then add 3 to both sides to get 3x ≥ -6, and divide by 3 to find x ≥ -2.

Front

How do you graph the solution set of an inequality?

Back

To graph the solution set of an inequality, draw a number line, and use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the region that represents the solution.

Front

What does it mean if x < 45?

Back

If x < 45, it means x can be any number less than 45, such as 44, 0, or -10.

Front

What is the first step in solving the inequality 2(x - 8) + 7 < -5(x + 2) - 3x - 19?

Back

The first step is to distribute the 2 and -5 to simplify the inequality.