8-6 Flashcard

Front

What is an inequality?

Back

An inequality is a mathematical statement that shows the relationship between two expressions that are not equal, using symbols like <, >, ≤, or ≥.

Front

How do you solve the inequality 25x + 175 ≤ 500?

Back

First, subtract 175 from both sides: 25x ≤ 325. Then, divide both sides by 25: x ≤ 13.

Front

What does the solution x ≤ 13 represent in the context of Cameron's mulch problem?

Back

It means Cameron can add up to 13 more bags of mulch to his truck without exceeding the weight limit.

Front

What is the first step to solve the inequality 3x - 19 < 17?

Back

Add 19 to both sides: 3x < 36.

Front

What is the solution to the inequality 3x - 19 < 17?

Back

x < 12.

Front

How do you interpret the solution x > 40 in the cellphone factory problem?

Back

The factory needs to produce more than 40 cellphones each day to earn more than $12,000.

Front

What is the mistake if a classmate says the solution to x/4 + 9 < 7 is x > -8?

Back

They flipped the inequality symbol even though they did not multiply or divide by a negative.

Front

What is the general form of a linear inequality?

Back

A linear inequality can be expressed in the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.

Front

What does the symbol '>' mean in an inequality?

Back

'>' means 'greater than' and indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' mean in an inequality?

Back

'<' means 'less than' and indicates that the value on the left is smaller than the value on the right.