Equations with variables on both sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

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

Back

To solve, first simplify both sides if necessary, then move all variable terms to one side and constant terms to the other side.

Front

What is the first step in solving the equation 3x + 5 = 2x + 10?

Back

Subtract 2x from both sides to get x + 5 = 10.

Front

What does it mean for two expressions to be equal?

Back

It means that the values of the expressions are the same for the same input.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the significance of the variable in an equation?

Back

The variable represents an unknown value that we are trying to solve for.

Front

In the context of shipping costs, how can you set up an equation to compare two companies' charges?

Back

Define the total cost for each company as a function of the weight, then set the two functions equal to each other.

Front

What is the formula for Company A's shipping cost based on weight?

Back

Cost_A = 7.25 + 0.20p, where p is the weight in pounds.

Front

What is the formula for Company B's shipping cost based on weight?

Back

Cost_B = 5.15 + 0.30p, where p is the weight in pounds.

Front

How do you find the point where two linear equations intersect?

Back

Set the two equations equal to each other and solve for the variable.