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Bell Work. 5 –9 –40 3. 1. 9 + (–4) 2. –3 – 6 3. 10(–4) 4. . One step equations. An equation is like a balance scale because it shows that two quantities are equal. What you do to one side of the equation must also be done to the other side to keep it balanced. ONE STEP EQUATIONS.

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one step equations1

An equation is like a balance scale because it shows that two quantities are equal.

What you do to one side of the equation must also be done to the other side to keep it balanced.

ONE STEP EQUATIONS
slide4

One way to solve an equation is to use inverse operations.

  • An inverse operation is an operation that “undoes”
  • another operation.
  • Addition and subtraction are inverse operations.
  • Multiplication and Division are inverse operations.
  • *Performing the same operation on each side of an
  • equation results in a new equation that has the same solution as the original equation.
one step equations2

To solve one step equations, you need to ask three questions about the equation:

  • What is the variable?
  • What operation is performed on the variable?
ONE STEP EQUATIONS
  • What is the inverse operation?

(The one that will undo what is being done to the variable)

one step equations3

Example 1 Solve x + 4 = 12

What is the variable?

The variable is x.

What operation is being performed on the variable?

Addition.

What is the inverse operation (the one that will undo what is being done to the variable)?

Subtraction.

Using the subtraction property of equality, subtract 4 from both sides of the equation.

The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONS

x + 4 = 12

- 4

- 4

x

=

8

one step equations4

Example 2 Solve y - 7 = -13

What is the variable?

The variable is y.

What operation is being performed on the variable?

Subtraction.

What is the inverse operation (the one that will undo what is being done to the variable)?

Addition.

Using the addition property of equality, add 7 to both sides of the equation.

The addition property of equality tells us to add the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONS

y - 7 = -13

+ 7

+ 7

y

=

-6

one step equations5

Example 3 Solve –6a = 12

What is the variable?

The variable is a.

What operation is being performed on the variable?

Multiplication.

What is the inverse operation (the one that will undo what is being done to the variable)?

Division

Using the division property of equality, divide both sides of the equation by –6.

ONE STEP EQUATIONS

The division property of equality tells us to divide the same thing on both sides to keep the equation equal.

–6a = 12

-6

-6

a

=

-2

one step equations6

Example 4 Solve

-10

=

What is the variable?

The variable is b.

What operation is being performed on the variable?

Division.

What is the inverse operation (the one that will undo what is being done to the variable)?

Multiplication

Using the multiplication property of equality, multiply both sides of the equation by 2.

The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONS

= -10

2 •

= -10

• 2

b

=

-20

slide10

6

–6

=

3

m

Remember!

Once you have solved an equation, it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation.

Solve:

m + 6 = 9

m + 6 = 9

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

slide11

You try:

-9 = y – 12

-9 + 12 = y – 12 + 12

y = 3

Check to see if you are correctIf y =3 is the solution…-9 = y – 12-9 = 3 – 12-9 = -9 solution checks!

slide12

You try:

-3x = 45

-3x ÷ -3 = 45÷ -3

X = -15

Check to see if you are correct…

-3x = 45

-3(-15) = 45

45 = 45 Yes!

slide13

You try:

c ÷ 2 = 13

2 x c = 13 x 2

c = 26

Check to see if you are correct…

Is 26 is the solution?

C÷2 = 13

26÷ 2 = 13

13 = 13 Yes it checks!

slide14

You try:

1. 3x = – 9

X = -3

-5x = -40

X = 8

try these on your paper
X - 7 = -1

-X = 9

10 = X + 3

Answers

6

-9

7

24

Try these on your paper.
slide16

Practice:

Worksheet