Module 3 Test

Front

What is the cost equation for Plan 1 of the dog-walking service?

Back

The cost equation for Plan 1 is: C = 3w + 10, where C is the total cost and w is the number of walks.

Front

What is the cost equation for Plan 2 of the dog-walking service?

Back

The cost equation for Plan 2 is: C = 5w, where C is the total cost and w is the number of walks.

Front

How do you find the number of walks when two plans cost the same?

Back

Set the cost equations equal to each other: 3w + 10 = 5w and solve for w.

Front

What does it mean for an equation to have infinitely many solutions?

Back

An equation has infinitely many solutions if it can be simplified to a true statement for all values of the variable, such as 0 = 0.

Front

What is the perimeter of a rectangle in terms of its length x?

Back

The perimeter P of a rectangle is given by P = 2(length + width). If width is expressed in terms of x, substitute accordingly.

Front

What is the significance of having one variable in an equation?

Back

Having one variable typically means there is a unique solution for that variable, assuming the equation is not contradictory.

Front

Back

The solution is x = 1.

Front

What does it mean for a variable to represent a length in a geometric context?

Back

A variable representing length must be non-negative, as lengths cannot be negative.

Front

Back

First, distribute and combine like terms, then isolate x to find the solution.

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.