solving equations. equations contain an equal sign (or inequality) and at least one variable

20
Solving Equations

Upload: ruth-garrison

Post on 22-Dec-2015

212 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solving Equations

Page 2: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solving Equations

Equations contain an equal sign (or inequality) and at least one variable.

Page 3: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

What is your Goal?

Find what value(s) make the equation true.

Page 4: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

How do you accomplish it?

Isolate the variable.Get rid of the furthest

number that is “with” the variable first.

Page 5: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve:Isolate the variable.

If added, then add the opposite

If multiplied, then multiply by the reciprocal

Page 6: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

How do you know you are correct?

Put your answer back into the original equation to see if both

side have the same value.

Page 7: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Questions to focus onWho is the variable?

Where is the variable?

Is the variable on the right side or left side of the equal sign?Combine like terms on the same side of the

equation

What numbers are with the variable?

(on the same side of the equal sign)

Which number is “furthest away” according to the Order of Operations? (P, E, M D, A S)

Page 8: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Questions to focus onHow is that number with the variable

(added or multiplied)?

How do you get rid of that number?

(Add opposite or Multiply by reciprocal)

Add the opposite or Multiply by the reciprocal to both sides of the equal sign!

Start over with the first question until the variable has been isolated.

Page 9: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve and check your answer.

2 3 33w

2 3w

5 w

Check:

2 5 3

2 2

Page 10: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve and check your answer.

5 5 105

y( ) ( )

105

y

50y

Check:

5010

5

Page 11: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve and check your answer. (2 operations)

3x + 5 = 20

3x + 5 – 5 = 20 – 5

3x = 15

3x = 15 3 3

x = 5

Check:

3(5) + 5 = 20

20 = 20

Page 12: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve and check your answer. (2 operations)

7 = 4 – 6x

7 – 4 = 4 – 4 – 6x

3 = -6x

3 = -6x -6 -6

-1/2 = x

Check:

7 = 4 – 6( )

7 = 4 – 6( -1/2 )

7 = 4 – -3

7 = 4 + 3

7 = 7

Page 13: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve and check your answer. (variables on the same side of equation)

5x + 2 – 4x = 6

5x – 4x + 2 = 6

1x + 2 = 6

x + 2 – 2 = 6 – 2

x = 4

Check:

5(4) + 2 – 4(4) = 6

20 + 2 – 16 = 6

22 – 16 = 6

6 = 6

Page 14: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve and check your answer. (variables on both sides of the equation)

4x – 7 = 6x + 2

4x + -4x + -7 = 6x + -4x + 2 -7 = 2x + 2

-7 + -2 = 2 + -2 -9 = 2x

-9 = 2x 2 2

-9/2 = x

Check:

4(-9/2) – 7 = 6(-9/2) + 2

-18 – 7 = -27 + 2

-18 + -7 = -27 + 2

-25 = -25

Page 15: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve and check your answer. (variables on 1 sides of the equation)

2x + 3(x – 4) = 13

2x + 3(1x + -4) = 13

2x + 3x + -12 = 13

5x + -12 = 13

5x + -12 + 12 = 13 + 12

5x = 25

5x = 25 5 5

x = 5

Check:

2(5) + 3((5) – 4) = 13

10 + 3(1) = 13

10 + 3 = 13

Page 16: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Your turn to try a few problems

Page 17: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Types of solutions:

No solution, there is no value for the variable that will make the equation true.

5 = 2

A unique answer, there is at least one value that makes the equation true.

x = number

Infinite number of solutions, all real numbers makes the equation true.

3 = 3

Page 18: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve for x.

x + 2 = x – 4

x – x + 2 = x – x – 4

2 = -4

No Solution

Page 19: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve for x.

2x – 1 = x + 5

2x – x – 1 = x – x + 5

x – 1 = 5

x – 1 + 1 = 5 + 1

x = 6 unique solution

Page 20: Solving Equations. Equations contain an equal sign (or inequality) and at least one variable

Solve for x.

x + 4 = 4 + x

x – x + 4 = 4 + x – x

4 = 4

Infinite number of solutions