Unit 2: Reasoning with Expressions, Equations, and Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

How do you represent a situation where a quantity must be at least a certain value?

Back

You can represent this situation using an inequality, for example, if a quantity must be at least 200, you would write it as x ≥ 200.

Front

What does the expression 500 - 25w ≥ 200 represent?

Back

This inequality represents the situation where Phoebe withdraws $25 each week from her savings, ensuring she has at least $200 left.

Front

How do you simplify the expression 9(-5x + 8)?

Back

To simplify, distribute 9: 9 * -5x + 9 * 8 = -45x + 72.

Front

What is the solution to the inequality 11 ≥ a?

Back

This means that the value of 'a' can be any number less than or equal to 11.

Front

What does the expression 4(-p - 6) simplify to?

Back

It simplifies to -4p - 24.

Front

What is the purpose of using variables in expressions and equations?

Back

Variables represent unknown values and allow us to formulate general statements and solve problems.

Front

What does it mean to solve an inequality?

Back

Solving an inequality means finding all values of the variable that make the inequality true.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

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

Back

You can substitute the solution back into the inequality to see if it holds true.