2x – (4 – 5x) = 3(x + 4) 1.) -4 + 5x – 4 + 5x =2x x # 2 5 7x -4 7x – 4 = 3x+12 3x + 12 -3x...
TRANSCRIPT
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