Equations and Inequalities with real-world scenarios

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?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be either less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be either greater than or equal to the value on the right.

Front

How do you represent a real-world scenario with an inequality?

Back

You identify the quantities involved, determine the relationship between them, and express it using an inequality symbol.

Front

What is the first step in solving an inequality?

Back

The first step in solving an inequality is to isolate the variable on one side of the inequality.

Front

If a truck can carry at most 1,600 pounds, how would you express the weight of boxes loaded into it?

Back

You would express it as an inequality: 50x + 400 ≤ 1,600, where x is the number of boxes.

Front

What does 'at most' mean in terms of inequalities?

Back

'At most' means that the value cannot exceed a certain limit, which is represented by the '≤' symbol.

Front

What is the solution to the inequality 25w + 200 > 750?

Back

To solve for w, subtract 200 from both sides: 25w > 550, then divide by 25: w > 22.

Front

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

Back

You can check by substituting the solution back into the original inequality to see if it holds true.

Front

What is a real-world example of using inequalities?

Back

A real-world example is budgeting, where you might have a limit on spending and need to express it as an inequality.