solving algebra equations objective: to solve all kinds of algebra equations

Solving Algebra Equations

Objective: To solve all kinds of algebra equations.

Solving Equations

• When solving algebraic equations, we will do the same things in the same order each time. Our goal is to isolate the variable. We will do this by getting all terms with letters (variables) on one side and all terms that are just numbers (constants) on the other. We will follow this procedure.

Solving Equations

1. We will get all terms with a variable on the one side and all terms without a variable on the other side. We will do this using addition and subtraction.

2. We will then make the variable have a coefficient of one. We will do this using multiplication and division.

Example 1

• Find the solution for the following equation.

1532 x

Example 1


• Subt 3 from both sides

• Divide both sides by 2

6

122315332

1532

212

22

x

xxx

x

Example 3


• When working with fractions, it is often easier to get rid of the fraction first. In this problem, we will do this by multiplying both sides by 3.

1237

x

Example 3


• When working with fractions, it is often easier to get rid of the fraction first. In this problem, we will do this by multiplying both sides by 3.

1237

x

312373

x

2973677

367

xxx

Class work

• Page 91• 11-21 odd• 27-33 odd

Homework

• 2• 38-50 all

Multi-Step Equations

• When solving more complex equations, you should always simplify each side of the equation first before you start to move things. Then, use our rules from before.

Example 1

• Solve the following equations.

mm 22355

Example 1


• Combine like terms• Add 23 to both sides

• Divide by 7• Solve

m

mm

mmm

m

4

72823237235

237522355

77

728

Got it?


226811 mm 14552 yy

Got it?


6

305822885

2285226811

530

55

m

mmm

mm

m

14552 yy

Got it?


6

305822885

2285226811

530

55

m

mmm

mm

m

3

93514553

145314552

39

33

y

yyy

yy

y

Example 3


36)12(8 x

Example 3


47

1628

1616

28168368816

3681636)12(8

x

xxxx

x

Example 4


• When solving equations with fractions, first find the common denominator. Then, multiply both sides by the common denominator to get rid of the fractions!

• What is the common denominator?

1034

3xx

Example 4


24

120512049

12101234

312

5120

55

x

xxx

xx

x

1034

3xx

3 4

Got it?


343

52

bb

365

91 m

Got it?


2360

2360

2323

602360158

2032043

5220

b

bbb

bb

b

365

91 m

343

52

bb

Got it?


2360

2360

2323

602360158

2032043

5220

b

bbb

bb

b

365

91 m

343

52

bb

m

mm

m

m

m

613

66

613

61361515152

6152

1836

5189118

Class Work

• Page 98• 12, 14, 16• 22, 24, 26• 32, 34, 36• 46, 48, 52

Homework

• Page 98• 21-37 odd• 45-53 odd

Variables on Both Sides

• When solving equations with variables on both sides, I like to get the variables on the left side and the constants on the right.

14225 xx

Variables on Both Sides

• When solving equations with variables on both sides, I like to get the variables on the left side and the constants on the right.

4

123214223

14232142225

312

33

x

xxx

xxxx

x

14225 xx

Example 3

• Solve the following equation. Remember, we will simplify each side first.

)11(3)15(2 xx

Example 3

• Solve the following equation. Remember, we will simplify each side first.

5

357233227

332733332310

333210)11(3)15(2

735

77

x

xxx

xxxxxxxx

x

Got it?


)13(2)12(4 yy )4(3)4(7 aa

Got it?


5

306426446

26462622428

26248)13(2)12(4

630

66

y

yyy

yyyyyyyy

y

)4(3)4(7 aa

Got it?


5

306426446

26462622428

26248)13(2)12(4

630

66

y

yyy

yyyyyyyy

y

4

40102812102828

12102812333728

123728)4(3)4(7

1040

1010

a

aa

aaaaa

aaaa

a

Strange Answers

• Sometimes after doing your work, you will get an answer that is different from most others.

• If you get a statement that is always true, the answer to the original problem is all solutions. This is called an identity.

Strange Answers

• Sometimes after doing your work, you will get an answer that is different from most others.

• If you get a statement that is always true, the answer to the original problem is all solutions. This is called an identity.

• If you get a statement that is always false, the answer to the original problem is no solution.

Problem 4

• Solve the following equation.

1212121010121010

12101210)65(21210

xxxxxxxx

Problem 4


• This statement is always true. This is an identity. The answer is all solutions.

1212121010121010

12101210)65(21210

xxxxxxxx

Problem 4


54599499

5949125349

mmmmmm

mmm

Problem 4


• This statement is always false. The answer is no solutions.

54599499

5949125349

mmmmmm

mmm

Class Work

• Pages 105-106• 10, 12, 14, 22, 24, 26, 28, 30, 32

Homework

• Pages 105-106• 11-17 odd• 21-37 odd

Literal Equations

• Solve for x. cbxax

Literal Equations

• Solve for x.

cbaxcbxax

)(

Literal Equations

• Solve for x.

bacx

bac

babax

cbaxcbxax

)()()()(

Got it?

• Solve the following equation for m. What is the value of m when n = -2?

nm 524

Got it?


• Add 5n to both sides

• Divide both sides by 2mnmn

nnmnnm

254

25455254

524

Got it?


• Add 5n to both sides

• Divide both sides by 2

• Replace n with -2.

mnmn

nnmnnm

254

25455254

524

326

2)10(4

2)2(54

Example 3

• Look at page 110. There are several formulas that you will be using. You should be familiar with most of these.

Example 3

• What is the radius of a circle with circumference 64 ft? Round to the nearest tenth.

rC 2

Example 3

• What is the radius of a circle with circumference 64 ft? Round to the nearest tenth.

r

rrrC

2.1022

264

2642

Class Work

• Page 112• 12, 14, 16,• 20, 22, 24

Homework

• Page 112• 11-17 odd

solving algebra equations objective: to solve all kinds of algebra equations

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