Solving and Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

How do you solve the inequality m - 9 ≤ 20?

Back

Add 9 to both sides to isolate m: m ≤ 29.

Front

What does the inequality 6 > x mean?

Back

It means that x is any number less than 6.

Front

How do you represent the solution set of an inequality on a number line?

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, and shade the appropriate direction.

Front

What is the solution set for the inequality m - 5 > -8?

Back

Add 5 to both sides: m > -3.

Front

Which number is a solution for the inequality 12 > x + 1?

Back

Subtract 1 from both sides: x < 11, so -5 is a solution.

Front

What does the symbol ≤ mean?

Back

It means 'less than or equal to'.

Front

What does the symbol > mean?

Back

It means 'greater than'.

Front

How do you graph the inequality x - (-4) < 8?

Back

First, simplify to x + 4 < 8, then x < 4. Graph with an open circle at 4 and shade left.

Front

What is the first step in solving the inequality 3x + 2 > 11?

Back

Subtract 2 from both sides: 3x > 9.