Warm Up Evaluate. 1.0.51 + (0.29) Give the opposite of each number. 3. 84. Evaluate each expression...

Warm UpEvaluate.1. 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 Evaluate each expression.

7.

8.

9.

0.8

23

–8

14 8

23

1

23

1.8

Solve one-step equations in one variable by using addition or subtraction. Solve one-step equations in one variable by using multiplication or division.

Objective

Vocabularyequationsolution of an equation

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.

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.

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.

Solve the equation. Check your answer.

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.


Try This!

Since 3.2 is subtracted from n, add 3.2 to both sides to undo the subtraction.

n – 3.2 = 5.6

+ 3.2 + 3.2

n = 8.8

Check n – 3.2 = 5.6

8.8 – 3.2 5.65.6 5.6

To check your solution, substitute 8.8 for n in the original equation.


Try This!

Since 6 is subtracted from k, add 6 to both sides to undo the subtraction.

–6 = k – 6 + 6 + 6

0 = k

Check –6 = k – 6

–6 0 – 6–6 –6

To check your solution, substitute 0 for k in the original equation.


Solving Equations by Using Subtraction

Since 17 is added to m, subtract 17 from both sides to undo the addition.

m + 17 = 33– 17 –17

m = 16

Check m + 17 = 33

16 + 17 3333 33

To check your solution, substitute 16 for m in the original equation.


Solving Equations by Using Subtraction

Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition.

4.2 = t + 1.8 –1.8 – 1.8

2.4 = t

Check 4.2 = t + 1.8

4.2 2.4 + 1.84.2 4.2

To check your solution, substitute 2.4 for t in the original equation.


Try This!

Since 5 is added to k, subtract 5 from both sides to undo the subtraction.

–5 = k + 5 – 5 – 5 –10 = k

Check –5 = k + 5

–5 –10 + 5–5 –5

To check your solution, substitute –10 for k in the original equation.


Try This!

Since 6 is added to t, subtract 6 from both sides to undo the addition.

6 + t = 14– 6 – 6

t = 8

Check 6 + t = 14

6 + 8 1414 14

To check your solution, substitute 8 for t in the original equation.

Remember that subtracting is the same as adding the opposite. When solving equations, you will sometimes find it easier to add an opposite to both sides instead of subtracting.

Solve the equation.

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

Solve the equation.

Solving Equations by Using Multiplication

Since n is divided by 6, multiply both sides by 6 to undo the division.n = 16.8

2.8 2.8

To check your solution, substitute 16.8 for n in the original equation.

= 2.8n6

2.8 16.86

Check = 2.8n6


Try This!

Since p is divided by 5, multiply both sides by 5 to undo the division.p = 50

10 10

To check your solution, substitute 50 for p in the original equation.

= 10p5

10 505

Check = 10p5


Try This!

Since y is divided by 3, multiply both sides by 3 to undo the division.–39 = y

–13 –13

To check your solution, substitute –39 for y in the original equation.

–13 =y3

–13 –393

yCheck –13 =

3


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 Using Division

Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.

0.8 = v

–4.8 –4.8

To check your solution, substitute 0.8 for v in the original equation.

–4.8 = –6v

–4.8 –6(0.8)

Check –4.8 = –6v


Try This!

Since c is multiplied by 4, divide both sides by 4 to undo the multiplication.

4 = c

16 16

To check your solution, substitute 4 for c in the original equation.

16 = 4c

16 4(4)

Check 16 = 4c


Try This!

Since k is multiplied by 15, divide both sides by 15 to undo the multiplication.k = 5

75 75

To check your solution, substitute 5 for k in the original equation.

15k = 75

15(5) 75

Check 15k = 75

Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.

Solve the equation.

Solving Equations That Contain Fractions

w = 24

20 20

To check your solution, substitute 24 for w in the original equation.

w = 2056

Check w = 2056

The reciprocal of is . Since w is

multiplied by , multiply both sides

by .

56

65

566

5

20

Solve the equation.

Solving Equations That Contain Fractions

= z3

16

To check your solution,

substitute for z in the

original equation.

32

= z32

18

The reciprocal of is 8. Since z is


by 8.

181

8

Check18

316

= z

316

316

Solve the equation. Check your answer.Try This!

– = b14

To check your solution,

substitute – for b in the

original equation.

54

15

The reciprocal of is 5. Since b is


by 5.

151

5

= b54–

= b5 4Check11–

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

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


WORDS

Multiplication Property of EqualityYou can multiply both sides of an equation by the same number, and the statement will still be true.

NUMBERS

6 = 6 6(3) = 6(3) 18 = 18

ALGEBRA a = b ac = bc


Properties of EqualityDivision Property of EqualityYou can divide both sides of an equation by the same nonzero number, and the statement will still be true.

WORDS

a = b (c ≠ 0)

8 = 8

2 = 2

ALGEBRA

NUMBERS 84

84

=

ac

ac=

Lesson QuizSolve each equation.

1. r – 4 = –8

2. m + 13 = 58

3. 0.75 = n + 0.6

4. –5 + c = 22

5.

6.8y = 4

7.126 = 9q

8.

–4

45

0.15

27

21

–14

40

Warm Up Evaluate. 1.0.51 + (0.29) Give the opposite of each number. 3. 84. Evaluate each expression...

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Transcript of Warm Up Evaluate. 1.0.51 + (0.29) Give the opposite of each number. 3. 84. Evaluate each expression...