Inequality Word Problems

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 word problem as an inequality?

Back

Identify the quantities involved, determine the relationship between them, and express that relationship using inequality symbols (>, <, ≥, ≤).

Front

What does the inequality 10 + 0.25x > 16 + 0.15x represent?

Back

It represents the condition under which Store A's engraving cost is greater than Store B's cost based on the number of letters x.

Front

How do you solve the inequality 1000 - 50x < 595 + 5x?

Back

Combine like terms: 1000 - 595 < 50x + 5x, which simplifies to 405 < 55x, then divide by 55 to find x.

Front

What is the significance of the solution to an inequality?

Back

The solution to an inequality indicates the range of values that satisfy the condition expressed by the inequality.

Front

What does the inequality x > 22 indicate in the context of weight gain?

Back

It indicates that after 22 months, James will weigh less than Joey, meaning he will have gained less weight over time.

Front

How do you interpret the inequality 5x ≥ 2x + 9?

Back

This means that five times a number x is at least as much as twice that number plus 9.

Front

What is the first step in solving the inequality 100 + 5x > 400 - 15x?

Back

Combine like terms by adding 15x to both sides and subtracting 100 from both sides.

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.

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.