2x – (4 – 5x) = 3(x + 4)1.)-4 + 5x

– 4 + 5x =2xx #

2

5

7x

-4

-4

7x – 4 =

3x+12

3x + 12

3x + 12-3x-3x

4x – 4 = 12

+4 +4

4x = 16

4 4

x = 4 BPHS

Agenda

CA Standards:4.0: Students simplify expressions before solving linear equations in one variable. 12.0: Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

Objectives:(1) Students simplify expressions use inverse operations to solve equations.

1.) Warm - Up

2.) Lesson Fractions #1 ppt.

3.) Assignment

For example:For example:

6 73

x

22 8

5x

Anytime you see a fractionfraction

FractionFraction FractionFraction

Pencils Down

16 1

3

x

Example 1:Example 1:

An easy way to solve equations with fractionsfractions, is to zapzap the equation with multiplicationmultiplication.

We need to zap that 3 with multiplicationmultiplication.

So multiplymultiply EVERYTHINGEVERYTHING by 3.

3●3

3

x36 31

zapzap

x 18 318 18x 21

Write

This!

1

131 36x

22 8

5x

Example 2:Example 2:

We need to zap that 5 with multiplicationmultiplication.

So multiplymultiply everything by 5.

5●5 2

5x

52 58

zapzap

2x 10 4010 102x 302 2

x 15

1

1

5 521 2 8x

52 3

3x

Try one:Try one:

We need to zap that 3 with multiplicationmultiplication.

So multiplymultiply everything by 3.

3●3 5

3x

32 33

zapzap

5x 6 96 65x 155 5

x 3

52 3

3x

1

1

3 351 2 3x

Equations with fractions

Two Examples:Two Examples:

3

2

3

4

7

5xExample 3:

2

1

3

1

4

1 xxExample 4:

When there is more than onemore than one fraction

3

21 2

3

21 4

3

2

3

4

7

5x

Example 3:Example 3: What #’s are in the denominatordenominator? 77 and 33

7●3 = 21

21● DistributeDistribute that number into EVERYTHINGEVERYTHING!

21 5

7x

1

3

1 1

7 7

5 4 23 7 7x

142815 x28 28

x15 4215 15

x 5

14 143

53

MultiplyMultiply those numbers.

4215

ReduceReduce the top and bottom.

DD CC MM AA DD

4

12 1

4

12 3

4

1

4

3

3

2x

You You trytry::

What #’s are in the denominatordenominator? 3 and 4

3●4 = 12

12● DistributeDistribute that number into EVERYTHINGEVERYTHING!

12 2

3x

1

4

1 1

3 3

2 3 14 3 3x

398 x9 9

x8 128 8

x 2

3 43

42

MultiplyMultiply those numbers.

128

ReduceReduce the top and bottom.

DD CC MM AA DD

24 1

2

124

3x

2

1

3

1

4

1 xx

Example 4:Example 4: What #’s are in the denominatordenominator? 4, 3 and 2

4●3●2 = 24

24● DistributeDistribute that number into EVERYTHINGEVERYTHING!

24 1

4x

1

6

1 1

8 12

1 16 1 18 2x x

1286 xx

1214 x14 14

x 7

6 62 72

MultiplyMultiply those numbers.

1214

ReduceReduce the top and bottom.

DD CC MM AA DD

x #

6

8

14x 0

30 2

5

130

2x

5

2

2

1

3

2 xx

You Try:You Try: What #’s are in the denominatordenominator? 3, 2 and 5

3●2●5 = 30

30● DistributeDistribute that number into EVERYTHINGEVERYTHING!

30 2

3x

1

10

1 1

15 6

10 152 1 6 2x x

121520 xx

1235 x35 35

x

MultiplyMultiply those numbers.

1235

ReduceReduce the top and bottom.

DD CC MM AA DD

x #

20

15

35x 0