Download 1.4 Rewrite Formulas and Equations

1.4
Rewrite Formulas and
Equations
Goal
Your Notes
p Rewrite and evaluate formulas and equations.
VOCABULARY
Formula
Solve for a variable
Literal equation
Example 1
Rewrite a formula
Solve the formula A 5 l p w for l. Then find the length
of a rectangle with a width of 11 feet and an area of
187 square feet.
Solution
Step 1 Solve the formula for l.
A5lpw
5l
Write area formula.
Divide both sides by
.
Step 2 Substitute the given value into the rewritten
formula.
l5
5
Substitute
for w.
Simplify.
The length of the rectangle is
12
Lesson 1.4 • Algebra 2 Notetaking Guide
for A and
feet.
Copyright © Holt McDougal. All rights reserved.
1.4
Rewrite Formulas and
Equations
Goal
Your Notes
p Rewrite and evaluate formulas and equations.
VOCABULARY
Formula An equation that relates two or more
quantities, usually represented by variables
Solve for a variable To rewrite a formula as an
equivalent equation with a different variable alone
on one side of the equation
Literal equation An equation in which some or all
of the coefficients and constants are indicated by
letters
Example 1
Rewrite a formula
Solve the formula A 5 l p w for l. Then find the length
of a rectangle with a width of 11 feet and an area of
187 square feet.
Solution
Step 1 Solve the formula for l.
A5lpw
A
w
} 5l
Write area formula.
Divide both sides by w .
Step 2 Substitute the given value into the rewritten
formula.
187
l5 }
11
5 17
Substitute 187 for A and
11 for w.
Simplify.
The length of the rectangle is 17 feet.
12
Lesson 1.4 • Algebra 2 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Your Notes
Checkpoint Complete the following exercises.
1. Solve the formula P 5 2l 1 2w for w. Then find the
width of a rectangle with a length of 9 meters and a
perimeter of 32 meters.
2. Solve the distance formula d 5 rt for t. Then find the
time it takes to travel the distance of 135 miles at a
rate of 30 miles per hour.
Example 2
Solve a literal equation
Solve the literal equation ax 1 b 5 c 1 d for x. Then
use your general solution to solve the equation
2x 1 15 5 5 1 7.
Solution
Step 1 Solve ax 1 b 5 c 1 d for x.
When you divide
both sides of an
equation by an
unknown, remember
to restrict the
quantity to nonzero
numbers to avoid
dividing by 0.
ax 1 b 5 c 1 d
ax 5 c 1 d 2
Write original equation.
Subtract
x5
from each side.
each side by
.
Step 2 Solve 2x 1 15 5 5 1 7 by substituting the given
values into the rewritten formula.
x5
Substitute
for a,
for
b,
for c, and
for d.
x5
Simplify.
Checkpoint Complete the following exercise.
3. Solve the literal equation ax 2 b 5 c for x. Then
use your general solution to solve the equation
4x 2 5 5 3.
Copyright © Holt McDougal. All rights reserved.
Lesson 1.4 • Algebra 2 Notetaking Guide
13
Your Notes
Checkpoint Complete the following exercises.
1. Solve the formula P 5 2l 1 2w for w. Then find the
width of a rectangle with a length of 9 meters and a
perimeter of 32 meters.
7 meters
2. Solve the distance formula d 5 rt for t. Then find the
time it takes to travel the distance of 135 miles at a
rate of 30 miles per hour.
4.5 hours
Solve a literal equation
Example 2
Solve the literal equation ax 1 b 5 c 1 d for x. Then
use your general solution to solve the equation
2x 1 15 5 5 1 7.
Solution
Step 1 Solve ax 1 b 5 c 1 d for x.
When you divide
both sides of an
equation by an
unknown, remember
to restrict the
quantity to nonzero
numbers to avoid
dividing by 0.
ax 1 b 5 c 1 d
ax 5 c 1 d 2 b
c1d2b
x5 }
a
Write original equation.
Subtract b from each side.
Divide each side by a .
Step 2 Solve 2x 1 15 5 5 1 7 by substituting the given
values into the rewritten formula.
5 1 7 2 15
x5 }
2
Substitute 2 for a, 15 for
b, 5 for c, and 7 for d.
x 5 2 1.5
Simplify.
Checkpoint Complete the following exercise.
3. Solve the literal equation ax 2 b 5 c for x. Then
use your general solution to solve the equation
4x 2 5 5 3.
c1b
x5}
a ; x52
Copyright © Holt McDougal. All rights reserved.
Lesson 1.4 • Algebra 2 Notetaking Guide
13
Your Notes
Rewrite a linear equation
Example 3
Solve 5x 2 4y 5 9 for y. Find y when x 5 23.
Step 1 Solve the equation for y.
5x 2 4y 5 9
When dividing each
side of an equation
by the same
number, remember
to divide every term
by the number.
Write original equation.
24y 5 9
Subtract
side.
1
y52
from each
Divide each side by
.
Step 2 Substitute the given value into the equation.
1
y52
Substitute 23 for x.
(23)
y5
Example 4
Simplify.
Rewrite a nonlinear equation
Solve 8y 1 xy 5 10 for y. Find y when x 5 26.
Step 1 Solve the equation for y.
8y 1 xy 5 10
y 5 10
10
y5
Write original equation.
Distributive property
Divide each side by
.
Step 2 Substitute the given value into the equation.
10
y5
5
Substitute 26 for x.
Checkpoint Solve the equation for y. Then find the
value of y when x 5 4.
Homework
14
4. 2y 1 6x 5 14
Lesson 1.4 • Algebra 2 Notetaking Guide
5. 3y 2 4xy 5 26
Copyright © Holt McDougal. All rights reserved.
Your Notes
Example 3
Rewrite a linear equation
Solve 5x 2 4y 5 9 for y. Find y when x 5 23.
Step 1 Solve the equation for y.
5x 2 4y 5 9
When dividing each
side of an equation
by the same
number, remember
to divide every term
by the number.
Write original equation.
24y 5 9 2 5x
Subtract 5x from each
side.
9
5
1 }
x
y52 }
4
4
Divide each side by 24 .
Step 2 Substitute the given value into the equation.
9
5
1 }
(23)
y52 }
Substitute 23 for x.
y 5 26
Simplify.
4
Example 4
4
Rewrite a nonlinear equation
Solve 8y 1 xy 5 10 for y. Find y when x 5 26.
Step 1 Solve the equation for y.
8y 1 xy 5 10
(8 1 x) y 5 10
10
y5
81x
Write original equation.
Distributive property
Divide each side by
81x .
Step 2 Substitute the given value into the equation.
10
y5
5 5
Substitute 26 for x.
8 1 (26)
Checkpoint Solve the equation for y. Then find the
value of y when x 5 4.
Homework
4. 2y 1 6x 5 14
y 5 7 2 3x; 25
14
Lesson 1.4 • Algebra 2 Notetaking Guide
5. 3y 2 4xy 5 26
26
y5}
; 22
3 2 4x
Copyright © Holt McDougal. All rights reserved.