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 'less than or equal to'.

Front

How do you solve the inequality 4x - 10 ≤ 22?

Back

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

Front

What does the solution x ≤ 8 represent on a number line?

Back

It represents all numbers to the left of 8, including 8 itself.

Front

What is the difference between an open circle and a closed circle on a graph?

Back

An open circle indicates that the number is not included (e.g., > or <), while a closed circle indicates that the number is included (e.g., ≥ or ≤).

Front

How do you graph the inequality 2x + 3 < 7?

Back

First, solve for x: 2x < 4, so x < 2. Graph with an open circle at 2 and shade to the left.

Front

What is the solution to the inequality -2x + 3(-4x + 6) ≤ 116?

Back

The solution is x ≥ -7.

Front

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

Back

The symbol '>' means 'greater than'.

Front

When solving inequalities, what happens when you multiply or divide by a negative number?

Back

When you multiply or divide by a negative number, you must reverse the inequality sign.

Front

What is the solution to the inequality x < 24?

Back

The solution represents all numbers less than 24.