SECTION 3.1Solving Equations Using Addition

and Subtraction.

TO SOLVE AN EQUATION MEANS...

To isolate the variable having a coefficient of 1 on one side of the

equation.

Ex: x = 5 is solved for x.

y = 2x - 1 is solved for y.

HERE IS AN EXAMPLE…1) SOLVE R + 16 = -7

Think of this equation as a balance scale.

Whatever you do to one side has to be done to the other to keep it balanced!

1) SOLVE R + 16 = -7

To solve, you must get the variable by itself!! What is the

variable? What number is on the same side as r?

+16To get r by itself, we must undo the “add 16”. What is the opposite of addition?

Subtract 16

- 16 -16

r = -23

-23 + 16 = -7

1) SOLVE R + 16 = -7

1. Draw a line to separate the equation into 2 sides

2. Subtract 16 from both sides

3. Simplify vertically

4. Check your answer by substituting your answer back into the problem

2) SOLVE X + 2 = -3GET THE VARIABLE BY ITSELF. WHAT IS YOUR FIRST STEP?

1. Add 2 to both sides

2. Subtract 2 from both sides

3. Add 3 to both sides

4. Subtract 3 from both sides

Answer Now

2) SOLVE X + 2 = -3

1. Draw a line to separate the equation into 2 sides

2. Subtract 2 from both sides

3. Simplify vertically

4. Check your answer by substituting your answer back into the problem

- 2 - 2

x = -5

-5 + 2 = -3

On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

3) SOLVE 8 = M - 3

1.m = 5

2.m = 11

3.m = 24

4.m = 8/3Answer Now

3) SOLVE 8 = M - 3

+ 3 + 3

11= m

8 = 11 - 3

1. Draw a line to separate the equation into 2 sides

2. Add 3 to both sides3. Simplify vertically4. Check your answer

by substituting your answer back into the problem

REMEMBER: WHEN SOLVING EQUATIONS, WE WANT TO ELIMINATE DOUBLE SIGNS.

y + (-3) = 8

is rewritten as

y – 3 = 8

p – (-5) = 6

is rewritten as

p + 5 = 6As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”. This will make things less confusing in the future!

Example 1

Example 2

4) SOLVE Y + (-3) = 7

y – 3 = 7

+ 3 +3

y = 10

10 + (-3) = 7

1. Draw a line to separate the equation into 2 sides

2. Eliminate the double sign

3. Add 3 to both sides4. Simplify vertically5. Check your answer

by substituting your answer back into the problem

5) SOLVE. X - (-2) = 1 x + 2 = 1

- 2 - 2

x = -1

x = -1

(-1) + 2 = 1

1. Draw a line to separate the equation into 2 sides

2. Eliminate the double sign3. Subtract 2 from both sides4. Simplify vertically5. We haven’t gotten x by

itself. If we read this aloud, it is “the opposite of x equals -1”. What would x be equal?

6. Check your answer

SOLVE Y – (-3) = 71. y = 10

2. y = 4

3. y = -10

4. y = -4

Answer Now

HOMEWORK:

9/9/13

Workbook page 13

Solving Equations by Adding or Subtracting