Inequalities word problems A.5

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing 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?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

How do you represent a situation where a person has a maximum budget?

Back

You can represent it using an inequality, such as: total cost ≤ budget.

Front

What is the first step in solving a word problem involving inequalities?

Back

Identify the variables and write an inequality that represents the situation described in the problem.

Front

How do you solve the inequality 5w + 50 ≥ 7w?

Back

Subtract 5w from both sides to get 50 ≥ 2w, then divide by 2 to find w ≤ 25.

Front

What does it mean to 'solve for x' in an inequality?

Back

It means to find the values of x that make the inequality true.

Front

What is the solution to the inequality x + 32 ≥ 80?

Back

Subtract 32 from both sides to get x ≥ 48.

Front

How can you check if a solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What is a real-world example of an inequality?

Back

A person has $50 to spend on groceries. If they want to buy apples at $3 each, the inequality would be: 3x ≤ 50, where x is the number of apples.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting from contradictory statements.