Exercise 19 Page 106

We have been asked to write and solve an equation in order to determine the length of the walls in the greenhouse. Since each section is of the same length, but we do not know this length, let x represent the length of each section.

Forming the Equation

On one wall, we have a 7 foot storage area and 5 equal sections x. Length_(Wall A)=7+5x The opposite wall has a 4 foot storage area and 6 equal sections. Length_(Wall B)=4+6x Since the two walls are equal in length, we can set the two equal to each other. 7+5x=4+6x

Solving the Equation

In order to find the length of a wall, we need to first find the length of a planting section. We can find this information by solving the equation created above.

Checking Our Work

Now that we have solved the equation, we need to check our work. We do this by substituting the solution back into the equation for all instances of x.

While checking our work, we produced a statement that is always true. This means that we solved the equation correctly.

Finding the Length of the Walls

If x=3, then the length of each section is 3 feet. We can use substitution to find the length of the walls.

The length of Wall A is 22 feet. Since the walls are the same length, the length of each wall is 22 feet.