What time is it?

Time to solve equations!

Chapter 2: Section 1

Solving One-Step Equations

What is our goal?

When we solve equations we want to isolate the variable to discover its value.

We want to find out how much the variable equals.

Solution of the Equation: the value of the variable that makes the equation true

Properties of Equality

Addition: If you add the same number to each side of an equation, the two sides remain equal.

ab

a c b c

14 9 5

14 3 9 5 3

Properties of Equality

Addition (cont.): If you add the same negative number to each side of an equation, the two sides remain equal.

ab

a ( c) b ( c)

10 9 1

10 ( 3) 9 1 ( 3)

So, how are we supposed to use these properties to solve equations?

1410 m

1414

24m141024

What is the additive inverse of -10?10

So what should we add to both sides?

10, so we are going to add 10 to both sides. This allows us to use the additive inverse and identity and then isolate the variable.

Now check your work and see if it checks out!!!

m 10 10 14 10

m 0 24

How ‘bout another example?

712 t

1212

t19

71912

What is the additive inverse of -7?7

What should we add to both sides?

7, so we are going to add it to both sides. This allows us to use the additive inverse and identity. Therefore, we isolate the variable.

Now check your work and see if it checks out!!!

12 7 t 7 7

19 t 0

Now you try

132 f

12

11x

15f

39 v 12v

3

2

4

1x

1913 g 32g

Let’s look at some examples

219 m

2121

12m

21912

What is the additive inverse of 9?-9

What should we add to both sides?

-9, so we are going to add -9 to both sides. This allows us to use the additive inverse and identity and isolate the variable.

Now check your work and see if it checks out!!!

m 9 ( 9) 21 ( 9)

m 0 12

This one is a bit tricky!!!

107 y

1010

17y

10717

What is the additive inverse of 7?-7

What do we add to both sides?

-7, so we are using the additive inverse and identity to isolate the variable.

Now check your work and see if it checks out!!!

y 7 ( 7) 10 ( 7)

y 0 17

Your Turn

7

1

721

147

3

3

1 v

21

16

77 y

1114 l

105 h

25 5

13

10

9

Can you find your answer?

Properties of Equalities (continued)

Multiplication: If you multiply each side of an equation by the same number (this number cannot be zero) then the two sides of the equation remain the same

ab

a c b c

6

23

6

2 2 3 2

Properties of Equalities (continued)

Multiplication (again): if you multiply each side of an equation by the same fraction (usually a reciprocal) then the two sides of the equation remain the same.

ab

1

c ab

1

c

12 3 4

1

212 3 4

1

2

Let’s look at some examples

453 y

1

3 3y 45

1

3

y 15

First thing you need to do is isolate the variable. In order for us to do this we simply multiply both sides by the multiplicative inverse of the coefficient.

What is the multiplicative inverse of 3?

Simplify.

1/3, so we multiply both sides by 1/3.

We have used the multiplicative inverse and identity to isolate the variable.

1

1

1

15

1 y 15

Can we have another?

9

4

g

4)9(4

4

g

36g

First thing you need to do is isolate the variable. What is the multiplicative inverse of 1/4?

4, so we multiply by 4 on both sides, what you do on one side you must do to the other

1

1

One more please

t

6

15

t

6

1

1

6)5(6

30 t

First thing you need to do is isolate the variable. What is the multiplicative inverse of -1/6?

-6, So now we multiply by the reciprocal on both sides; what you do on one side you must do to the other.

We have used the multiplicative inverse and identity to isolate the variable and solve the equation.

1

1

30 1 t

Your Turn!!!

8

4t

256

5a

x 48

a30

t 32

x4

336

4y 28

y 7

Finally, Your Assignment

Page 77 #2-20 even, 71, and 81 #21-51 multiples of 3, 70, and 82