Solving Equations with Variables on Both Sides

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity.

Front

How do you find the unit rate from a total cost?

Back

To find the unit rate, divide the total cost by the total quantity. For example, if 3 pounds of granola cost $3.75, the unit rate is $3.75 ÷ 3 = $1.25 per pound.

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can make the equation true. For example, x + 2 = x + 4 has no solution because simplifying leads to a contradiction.

Front

How do you solve an equation with variables on both sides?

Back

To solve an equation with variables on both sides, first, isolate the variable by moving all terms involving the variable to one side and constant terms to the other side.

Front

What is the first step in solving the equation x + 2 = x + 4?

Back

The first step is to subtract x from both sides, which simplifies the equation to 2 = 4, indicating no solution.

Front

How do you calculate the total cost when buying in bulk?

Back

To calculate the total cost when buying in bulk, determine the unit price and multiply it by the number of units purchased. For example, if hamburger costs $2 per pound and you buy 10 pounds, the total cost is $2 × 10 = $20.

Front

What is the fixed cost in a business equation?

Back

The fixed cost is the cost that does not change regardless of the number of goods produced or sold. In the teddy bear example, the fixed cost is $1500 per day.

Front

What is a variable cost in a business context?

Back

A variable cost changes with the level of output. In the teddy bear example, the variable cost is $8 for each teddy bear produced.

Front

How do you set up an equation to find break-even points?

Back

To find break-even points, set the total cost equal to total revenue. For example, 1500 + 8t = 12t represents the break-even point for the teddy bear company.

Front

What does it mean to compare unit prices?

Back

Comparing unit prices involves calculating the cost per unit of different products to determine which is the better buy. For example, comparing the cost of a 12-pack vs. a 6-pack of Pepsi.