solving equations by adding or subtracting objective: solve equations using the addition and...

Solving Equations by Adding or Subtracting

Objective: Solve equations using the addition and

subtraction properties of equalities.

Subtraction Property of Equality

For any numbers a, b, and c, if a =b, then a – c = b – c.

Example 1Solve x + 9 = 5. Check your solution.

Example 1Solve x + 9 = 5. Check your solution.

x + 9 = 5 -9 -9 Subtract 9 from each side

Example 1Solve x + 9 = 5. Check your solution.

x + 9 = 5 – 9 - 9 Subtract 9 from each side. x = -4

Check: x + 9 = 5

Example 1Solve x + 9 = 5. Check your solution.

x + 9 = 5 – 9 - 9 Subtract 9 from each side. x = -4

Check: x + 9 = 5 -4 + 9 ? 5 Replace x with -4.

Example 1Solve x + 9 = 5. Check your solution.

x + 9 = 5 – 9 - 9 Subtract 9 from each side. x = -4

Check: x + 9 = 5 -4 + 9 ? 5 Replace x with -4. 5 = 5 The solution is x = -4.

Addition Property of Equality

For any numbers a, b, and c, if a =b, then a + c = b + c.

Example 2Solve x - 4 = -1. Check your solution.

Example 2Solve x - 4 = -1. Check your solution.

x – 4 = -1 + 4 + 4 Add 4 to each side.

Example 2Solve x - 4 = -1. Check your solution.

x – 4 = -1 + 4 + 4 Add 4 to each side. x = 3

Example 2Solve x - 4 = -1. Check your solution.

x – 4 = -1 + 4 + 4 Add 4 to each side. x = 3

Check: x - 4 = -1

Example 2Solve x - 4 = -1. Check your solution.

x – 4 = -1 + 4 + 4 Add 4 to each side. x = 3

Check: x - 4 = -1 3 - 4 ? -1 Replace x with 3 -1 = -1 The solution is x = 3

1) Solve r + 16 = -7Think 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 number is on the same side as r?16

To 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 = -71. Draw “the river” 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 - 2 - 2

x = -5

-5 + 2 = -3

1. Draw “the river” to separate the equation into 2 sides

2. Subtract 2 from both sides

3. Simplify vertically4. Check your answer

by substituting your answer back into the problem

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 “the river” 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

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!

4) Solve y + (-3) = 7

y – 3 = 7

+ 3 +3

y = 10

10 + (-3) = 7

1. Draw “the river” 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

Assignment

• P. 112 #4-9, 16-21, 30, 33