Solving inequalities

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

How do you represent a situation where a total cost cannot exceed a certain amount?

Back

You can represent this situation using an inequality, such as: cost ≤ maximum amount.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

How do you solve the inequality 2x - 3 < -7?

Back

Add 3 to both sides: 2x < -4; then divide by 2: x < -2.

Front

What is set notation?

Back

Set notation is a way to describe a set of numbers that satisfy a certain condition, often written as {x | condition}.

Front

How do you graph the inequality x ≥ 5?

Back

Draw a number line, place a closed dot on 5, and shade to the right.

Front

What is the solution to the inequality 6x - 4 ≥ 26?

Back

x ≥ 5.

Front

How do you isolate x in the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, simplify: -2x - 12x + 18 ≤ 116; then combine like terms and solve for x.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that satisfy the inequality, often resulting in a contradiction.