Transcript 3-6: Solving Equations and Formulas

3-6: Solving Equations and Formulas
OBJECTIVE:
You will be able to solve equations and formulas for a specified variable.
This section introduces equations that we will solve using the steps
learned in sections 3-1 to 3-5.
However, the tricky part to this section is that some of the equations will
have other variables in them, rather than just one variable.
Having multiple variables is what differentiates these formulas from the
equations we have dealt with thus far.
In some ways, this is more confusing because we have to work with
letters and keep up with like terms instead of just getting plain numbers
together.
In other ways, this is easier to do because you are not getting to one
exact answer.
© William James Calhoun, 2001
3-6: Solving Equations and Formulas
EXAMPLE 1: Solve the equation -5x + y = -56
A. for y
B. for x
Write the equation.
What is on the same side as y?
-5x
Get rid of it by…
adding 5x to both sides.
And in a blink of an eye, you
are done.
-5x + y = -56
+5x
+5x
y = -56 + 5x
or
y = 5x - 56
Write the equation.
What is on the same side as x?
y and -5
Which is furthest from x?
y
Get rid of it first by...
subtracting y from both sides.
Divide through by -5.
-5x + y = -56
-y -y
-5x = -56 - y
-5
-5
Simplifying on the right hand
side can give you any one of
three different forms of an
answers.
 56  y
x
5
or
56  y
x
5
or
y  56
x
5
© William James Calhoun, 2001
3-6: Solving Equations and Formulas
EXAMPLE 2: Solve for y in 3y + z = am - 4y.
Write the equation.
Ask the questions to isolate y.
Move the y’s to the same side first.
Move the z.
Get rid of the 7 on the y.
3y + z = am - 4y
+4y
+4y
7y + z = am
-z -z
7y = am -z
7
7
am  z
y
7
Most real-world math problems involve formulas. In some cases, you
might need to re-arrange the formulas to meet specific needs.
The next example is one such case.
© William James Calhoun, 2001
3-6: Solving Equations and Formulas
EXAMPLE 3:
1.2 W
P

The formula
H 2 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 in (lb/in2), W represents the weight of the person wearing the show 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/ inch wide.
1.2 W 1.2(130lb ) 156lb
2
P


2
2
2
2 = 624 lb/in
H
0.25in
1


 in 
2 
B. Solve the formula for W.
1.2 W
H2
 1.2W 
H 2 P    2 H 2
 H 
H 2 P  1.2 W
H 2 P 1.2W

1.2
1.2
H 2P
W
1 .2
P
C. Find the weight of the person if the heel is 3
inches wide and the pressure exerted is 40 lb/in2.
H 2 P (3in ) 2 40lb / in 2 9in 2 40lb / in 2 


W
1.2
1.2
1 .2
940lb 
360lb


= 300 lb
1.2
1.2
© William James Calhoun, 2001
3-6: Solving Equations and Formulas
HOMEWORK
Page 175
#11 - 25 odd
© William James Calhoun, 2001