Equations and Inequalities Review

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 situation where a person needs to save money over time using an inequality?

Back

You can represent it by setting up an inequality that includes the amount already saved, the amount saved per time period, and the total amount needed.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the left side of the inequality can be either greater than or equal to the right side.

Front

In the context of saving money, how would you express the total amount saved after 'w' weeks if you save $50 per week?

Back

The total amount saved after 'w' weeks can be expressed as 50w, where 'w' is the number of weeks.

Front

If Remington has $1,800 and needs at least $3,000, how would you set up the inequality to find out how many weeks he needs to save?

Back

The inequality would be set up as 1,800 + 50w ≥ 3,000.

Front

What is the first step to solve the inequality 1,800 + 50w ≥ 3,000?

Back

The first step is to isolate the variable term by subtracting 1,800 from both sides of the inequality.

Front

After isolating the variable in the inequality 1,800 + 50w ≥ 3,000, what is the resulting inequality?

Back

The resulting inequality is 50w ≥ 1,200.

Front

How do you solve the inequality 50w ≥ 1,200 for 'w'?

Back

To solve for 'w', divide both sides of the inequality by 50, resulting in w ≥ 24.

Front

What does the solution w ≥ 24 indicate in the context of the problem?

Back

It indicates that Remington needs to save for at least 24 weeks to have enough money to buy the car.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear expression, which can be written in the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.