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1. -3(4x – 8) +7(-4 + 3x)

2. -4n(2n + 3) – 2n(1 + 2n)

HW Solutions

14. 17x + 4y

15. 3a + 13b + 2c

17. -4p – 2q

19. 13x + 4y

23. 15x + 10y

24. 11.8a + 8.8b

26. 9s – 16.2t – 14.4

ObjectiveThe student will be able to:

solve equations using addition and subtraction.

solve equations using multiplication and division.

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

5) Solve. -x - (-2) = 1

-x + 2 = 1

- 2 - 2

-x = -1

x = 1

-(1) + 2 = 1

1. Draw “the river” 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

6) Solve. -5t = 60To get the variable by itself, which

number needs to be moved?

-5

To move the -5, you have to do the opposite operation. What operation

will we use?

division

6) Solve -5t = 60 -5 -5

t = -12

-5(-12) = 60

1. Draw “the river” to separate the equation

into 2 sides

2. Divide both sides by -5

3. Simplify

4. Check your answer

7) Solve 15 = 6n 6 6

2.5 = n

15 = 6(2.5)

1. Draw “the river”

2. Divide both sides by 6

3. Simplify

4. Check your answer

8) Solve -3v = -1291. v = -126

2. v = -43

3. v = 43

4. v = 126

Answer Now

9) Solve

You don’t like fractions? Let’s get rid of them!

“Clear the fraction”

by multiplying both sides of the equation by the denominator.

x

4 12

9) Solve x

4 12

4 · · 4

x = -48

1. Draw “the river”

2. Clear the fraction – multiply both sides by 4

3. Simplify

4. Check your answer

x

4 12

248

14

3 · = 18 · 3

2x = 54

2 2

x = 27

1. Draw “the river”

2. Clear the fraction – multiply both sides by 3

3. Simplify

4. Divide both sides by 2

5. Simplify

6. Check your answer

10) Solve = 18 2x

32x

3

2( )2718

3

11) Which step clears the fraction in

312

5

b

1. Multiply by 3

2. Multiply by 5

3. Multiply by -12

4. Multiply by -5

Answer Now

12) Solve 4

87

b

1. b = -56

2. b = -14

3. b = 14

4. b = 56

Answer Now