What you should learn

To solve equations and formulas for a specified variable

NCTM Curriculm Standards 2 - 4, 6 - 9

 

Introduction: Some equations contain more than one variable. At times you will need to solve these equations for one of the variables. For example, suppose the variables x, y, and z were all in the same equation. To solve for x would mean to get x by itself on one side of the equation, with no x's on the other side. In the same way, to solve for y would mean to get y by itself on one side of the equation, with no y's on the other side.

The formula for the area of a triangle is A = (bh)/2 where b represents the length of the base and h represents the height of the triangle. Suppose you know the areas and the lengths of the bases of several triangles and you want to fidn the height of each triangle. Rather than solve the formula over and over for different values of A and b, it would be easier to solve the formula for h before substituting the values for the other variables.

A = (bh)/2

2A = 2[(bh)/2]

2A = bh

(2A)/b = (bh)/b

(2A)/b = h

When you divide by a variable in an equation, remember that division by 0 is undefined. For example, in the formula above, b cannot equal zero.

Exercise 1: Solve the equation -5x + y = -56

a. for y

-5x + y = -56

-5x + 5x +y = -56 + 5x

y = -56 + 5x

b. for x

Exercise 2: Solve for y in 3y + z = am - 4y

Many real-world problems require the use of formulas. When using formulas, you may need to use dimensional analysis. You may also be asked to solve the formula for a specific variable. This may make it easier to use certain formulas.

Exercise 3: The formula P = (1.2W)/H represents the amount of pressure exerted on the floor by the heel of a shoe. In this formula, P represents the pressure in pounds per square inch (lb/in), W represents the weight of a person wearing the shoe in pounds, and H is the width of the heel of the shoe in inches.

a. Find the amount of pressure exerted if a 130-pound person wore shoes with heels 1/2 inch wide.

P = (1.2W)/H

= (1.2 * 130)/ (1/2)

= (156)/(1/4)

= 624 lb/in

624 lb/in of pressure are exerted.

b. Solve the formula for W.

c. Find the weight of the person if the heel is 3 inches wide and the pressure exerted is 40lb/in.

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 11 - 33 odd, 35 - 41

Alternative Homework: Enriched: 12 - 30 even, 31 - 41

Extra Practice: Students book page 763 Lesson 3-6

Extra Practice Worksheet: Click Here.

Return to Chapter 3