Solving
Equations
by by
Solving
Equations
Adding
or Subtracting
Adding
or Subtracting
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Warm Up
Evaluate.
2
1.  2 + 4 1 3
3
3
3
2. 0.51 + (0.29) 0.8
Give the opposite of each number.
2 2
3. 8 –8
4. 
3 3
Evaluate each expression for a = 3 and b = 2.
5. a + 5 8
Holt McDougal Algebra 1
6. 12  b 14
Solving Equations by
Adding or Subtracting
Warm Up
Evaluate each expression.
1. (–7)(2.8) 19.6
2. 0.96 ÷ 6 0.16
3. (–9)(–9) 81
4.
1
5.
2
3
6.
1.8
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Essential Questions
How can you solve one-step equations
in one variable by using addition or
subtraction?
How can you solve one-step equations
in one variable by using multiplication
or division?
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Vocabulary
equation
solution of an equation
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
An equation is a mathematical statement
that two expressions are equal.
A solution of an equation is a value of the
variable that makes the equation true.
To find solutions, isolate the variable. A
variable is isolated when it appears by itself
on one side of an equation, and not at all on
the other side.
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Isolate a variable by using inverse operations which
"undo" operations on the variable.
An equation is like a balanced scale. To keep the
balance, perform the same operation on both sides.
Inverse Operations
Operation
Inverse Operation
Addition
Subtraction
Subtraction
Holt McDougal Algebra 1
Addition
Solving Equations by
Adding or Subtracting
Example 1B: Solving Equations by Using Addition
Solve the equation. Check your answer.
5 =z– 7
7
7
Since
is
subtracted
from
z,
add
to
16
16
16
16
both sides to undo the subtraction.
+ 7
+ 7
16
16
3=z
4
5 =z– 7
16
16
Check
To check your solution,
5
3 – 7
3
substitute
for z in the
4 16
16
4
original equation.
5
5

16 16
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Example 1A: Solving Equations by Using Addition
Solve the equation. Check your answer.
y – 8 = 24
+8 +8
y = 32
Check
Since 8 is subtracted from y, add 8 to
both sides to undo the subtraction.
y – 8 = 24
32 – 8
24
24
24 
Holt McDougal Algebra 1
To check your solution,
substitute 32 for y in the
original equation.
Solving Equations by
Adding or Subtracting
Check It Out! Example 4
A person's maximum heart rate is the highest
rate, in beats per minute, that the person's
heart should reach. One method to estimate
maximum heart rate states that your age
added to your maximum heart rate is 220.
Using this method, write and solve an
equation to find a person's age if the person's
maximum heart rate is 185 beats per minute.
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Check It Out! Example 4 Continued
age
added
to
a
+
a + r = 220
a + 185 = 220
– 185 – 185
a = 35
maximum
heart rate
r
is
220
=
220
Write an equation to represent the
relationship.
Substitute 185 for r. Since 185 is
added to a, subtract 185 from both
sides to undo the addition.
A person whose maximum heart rate is 185 beats per
minute would be 35 years old.
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Example 4: Application
Over 20 years, the population of a town
decreased by 275 people to a population of
850. Write and solve an equation to find the
original population.
decrease
current
original
in
minus
is
population
population
population
p
–
d
=
c
p – 275 =850
Substitute 275 for d and 850 for c.
p – 275 = 850
+ 275 + 275
p =1125
Since 275 is subtracted from p, add
275 to both sides to undo the
subtraction.
Holt McDougal Algebra 1
The original population was 1125 people.
Solving Equations by
Adding or Subtracting
Solving an equation that contains multiplication or
division is similar to solving an equation that
contains addition or subtraction. Use inverse
operations to undo the operations on the variable.
Inverse Operations
Operation
Multiplication
Division
Holt McDougal Algebra 1
Inverse Operation
Division
Multiplication
Solving Equations by
Adding or Subtracting
Example 1A: Solving Equations by Using
Multiplication
Solve the equation.
j
–8 =
3
Since j is divided by 3,
multiply both sides by 3
to undo the division.
–24 = j
Check
j
–8 =
3
–24
–8
3
–8 –8 
Holt McDougal Algebra 1
To check your solution,
substitute –24 for j in the
original equation.
Solving Equations by
Adding or Subtracting
Example 2A: Solving Equations by Using Division
Solve the equation. Check your answer.
9y = 108
y = 12
Check
Since y is multiplied by 9,
divide both sides by 9 to
undo the multiplication.
9y = 108
9(12)
108
Holt McDougal Algebra 1
108 To check your solution,
substitute 12 for y in the
108 
original equation.
Solving Equations by
Adding or Subtracting
Check It Out! Example 3b
Solve the equation.
4j = 2
3
6
j=1
Holt McDougal Algebra 1
4j
is the same as 4 j.
6
6
The reciprocal of 4 is 6 . Since j is
6
4
4
multiplied by , multiply both sides
6
6
by .
4
Solving Equations by
Adding or Subtracting
Example 4: Application
Ciro puts 1
4 of the money he earns from mowing
lawns into a college education fund. This year
Ciro added $285 to his college education fund.
Write and solve an equation to find how much
money Ciro earned mowing lawns this year.
one-fourth
times
earnings
equals
college fund
Write an equation to represent the relationship.
Substitute 285 for c. Since m is divided
by 4, multiply both sides by 4 to undo
the division.
m = $1140
Holt McDougal Algebra 1
Ciro earned $1140 mowing lawns.
Solving Equations by
Adding or Subtracting
Check it Out! Example 4
The distance in miles from the airport that a plane
should begin descending, divided by 3, equals the
plane's height above the ground in thousands of
feet. A plane began descending 45 miles from the
airport. Use the equation to find how high the
plane was flying when the descent began.
Distance
divided by 3
equals
height in thousands of feet
Write an equation to represent the
relationship.
Substitute 45 for d.
15 = h
The plane was flying at 15,000 ft when the descent began.
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Properties of Equality
WORDS
Addition Property of Equality
You can add the same number to both
sides of an equation, and the statement
will still be true.
NUMBERS
ALGEBRA
Holt McDougal Algebra 1
3=3
3+2=3+2
5=5
a=b
a+c=b+c
Solving Equations by
Adding or Subtracting
Properties of Equality
WORDS
Subtraction Property of Equality
You can subtract the same number from
both sides of an equation, and the
statement will still be true.
NUMBERS
ALGEBRA
Holt McDougal Algebra 1
7=7
7–5=7–5
2=2
a=b
a–c=b–c
Solving Equations by
Adding or Subtracting
Lesson Quiz
Solve each equation.
1. r – 4 = –8
–4
2.
3. m + 13 = 58
45
4. 0.75 = n + 0.6 0.15
5. –5 + c = 22
27
6. This year a high school had 578 sophomores
enrolled. This is 89 less than the number enrolled
last year. Write and solve an equation to find the
number of sophomores enrolled last year.
s – 89 = 578; s = 667
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Lesson Quiz: Part 1
Solve each equation.
1.
21
2.
2.8
3. 8y = 4
4. 126 = 9q –14
5.
40
6.
Holt McDougal Algebra 1
Solving Equations by
Adding or Subtracting
Lesson Quiz: Part 2
9
7. A person's weight on Venus is about
10
his or
her weight on Earth. Write and solve an equation
to find how much a person weighs on Earth if he
or she weighs 108 pounds on Venus.
Holt McDougal Algebra 1