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Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Solving Equations by Adding or Subtracting
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Warm UpEvaluate.
1. + 4
2. 0.51 + (0.29)
Give the opposite of each number.
3. 8 4.
Evaluate each expression for a = 3 and b = 2.
5. a + 5 6. 12 b
0.8
13
23
23
3 23
–8
14 8
23
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Warm UpEvaluate each expression. 1. (–7)(2.8)
2. 0.96 ÷ 6
3. (–9)(–9)
4.
5.
6.
19.6
0.16
1
81
23
1.8
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
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?
Essential Questions
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
equationsolution of an equation
Vocabulary
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
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.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Inverse Operations
Operation Inverse Operation
Addition Subtraction
Subtraction Addition
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.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Solve the equation. Check your answer.
Example 1B: Solving Equations by Using Addition
= z34
To check your solution, substitute for z in the original equation.
34
+ 716
+ 716
= z – 716
516
Check= z – 7
16 516
34
516
716
–
516
516
Since is subtracted from z, add to
both sides to undo the subtraction.
716
716
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Solve the equation. Check your answer.
Example 1A: Solving Equations by Using Addition
Since 8 is subtracted from y, add 8 to both sides to undo the subtraction.
y – 8 = 24 + 8 + 8
y = 32
Check y – 8 = 24
32 – 8 2424 24
To check your solution, substitute 32 for y in the original equation.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
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.
Check It Out! Example 4
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Check It Out! Example 4 Continued
a + r = 220
ageadded to
220maximum heart rate is
Write an equation to represent the relationship.
– 185 – 185
a = 35
a + 185 = 220 Substitute 185 for r. Since 185 is added to a, subtract 185 from both sides to undo the addition.
a + r = 220
A person whose maximum heart rate is 185 beats per minute would be 35 years old.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
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.
Example 4: Application
Substitute 275 for d and 850 for c.
+ 275 + 275
p =1125
p – d = c
original population minus
current population
decrease in
populationis
p – 275 = 850 Since 275 is subtracted from p, add 275 to both sides to undo the subtraction.
p – 275 =850
The original population was 1125 people.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Inverse Operations
Operation Inverse Operation
Multiplication Division
Division Multiplication
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.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Solve the equation.
Example 1A: Solving Equations by Using Multiplication
Since j is divided by 3, multiply both sides by 3 to undo the division.–24 = j
–8 –8
To check your solution, substitute –24 for j in the original equation.
–8 =j3
–8 –243
Check –8 =j3
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Solve the equation. Check your answer.
Example 2A: Solving Equations by Using Division
Since y is multiplied by 9, divide both sides by 9 to undo the multiplication.y = 12
108 108
To check your solution, substitute 12 for y in the original equation.
9y = 108
9(12) 108
Check 9y = 108
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Check It Out! Example 3b
j = 1
Solve the equation.
=4j6
23
is the same as j.46
4j6
The reciprocal of is . Since j is
multiplied by , multiply both sides
by .
464
6
64
64
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Example 4: Application
Write an equation to represent the relationship.
Ciro puts 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.
14
one-fourth times earnings equals college fund
m = $1140
Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division.
Ciro earned $1140 mowing lawns.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Check it Out! Example 4
Write an equation to represent the relationship.
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
15 = h
Substitute 45 for d.
The plane was flying at 15,000 ft when the descent began.
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
WORDS
Addition Property of EqualityYou can add the same number to both sides of an equation, and the statement will still be true.
NUMBERS
3 = 3 3 + 2 = 3 + 2 5 = 5
ALGEBRA a = b a + c = b + c
Properties of Equality
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
WORDS
Subtraction Property of EqualityYou can subtract the same number from both sides of an equation, and the statement will still be true.
NUMBERS
7 = 7 7 – 5 = 7 – 5 2 = 2
ALGEBRA a = b a – c = b – c
Properties of Equality
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Lesson QuizSolve each equation.
1. r – 4 = –8
2.
3. m + 13 = 58
4. 0.75 = n + 0.6
5. –5 + c = 22
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.
–4
45
0.15
27
s – 89 = 578; s = 667
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Lesson Quiz: Part 1Solve each equation.
1.
2.
3. 8y = 4
4. 126 = 9q
5.
6.
21
2.8
–14
40
Solving Equations by Adding or Subtracting
Holt McDougal Algebra 1
Lesson Quiz: Part 2
7. A person's weight on Venus is about 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.
910