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

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

Back

'At most' means that a value can be equal to or less than a certain number. In inequality terms, it is represented as \( \leq \).

Front

How do you represent 'x is at most 30' in inequality form?

Back

The inequality is represented as \( x \leq 30 \).

Front

What does 'under' mean in terms of inequalities?

Back

'Under' means that a value must be less than a certain number. In inequality terms, it is represented as \( < \).

Front

How do you represent 'Wes wants to spend under $15 on lunch' in inequality form?

Back

The inequality is represented as \( 2.50p + 1.75 < 15 \), where \( p \) is the number of pizza slices.

Front

What is the first step to solve an inequality?

Back

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

Front

What does 'more than' mean in terms of inequalities?

Back

'More than' means that a value must be greater than a certain number. In inequality terms, it is represented as \( > \).

Front

How do you represent 'Stacy wants to have more than $150 in her account' in inequality form?

Back

The inequality is represented as \( 25 + 0.50x > 150 \), where \( x \) is the number of lemonade cups sold.

Front

What is the solution to the inequality \( 6.89 + 0.59x \leq 8.50 \)?

Back

To solve, subtract 6.89 from both sides: \( 0.59x \leq 1.61 \). Then divide by 0.59: \( x \leq \frac{1.61}{0.59} \approx 2.73 \). Thus, \( x \) can be at most 2 pens.

Front

What does 'less than' mean in terms of inequalities?

Back

'Less than' means that a value must be smaller than a certain number. In inequality terms, it is represented as \( < \).