Ch 3.1

Objective:

To solve simple, one-step variable equations

DefinitionEquationA balanced statement of equalitybetween two quantities.One Step Only one operation is performed (+, -, *, ÷)

4 + 3 = 7

fulcrum

4 + 3 7=

1) Goal: Isolate the variable.

2) Undo operations with their opposite operation.

3) Always do the same thing to both sides of the equation.

fulcrum

4 + 3 7=- 3

fulcrum

4 7=

fulcrum

4 7=

fulcrum

47=

4 + 3 7=- 3 - 3

4 4=

Perform the same operation to both sides to keep the equation balanced.

x + 6 11=

This property can be used to solve variable equations.

-6 -6

x 5=

x + 6 = 11-6 -6x = 5

Algebraic Approach

Solve.

1) m + 2 = 10

2) x - 4 = 6

3) x + 7 = 3

4) m - 4 = 9

5) 11 = x - -2

6) 8 + y = -6

-2 -2m = 8

+4 +4x = 10

-7 -7x = -4

+4 +4m = 13

-2 -29 = x

-8 -8y = -14

Solve.

1) -4 + x = 15

2) 7 = x + 13

3) -10 = 6 + x

4) - 4 = m + 9

5) 9 + 7 = x

6) y = 8 - 13

+4 +4x = 19

-13 -13-6 = x

-6 -6-16 = x

-9 -9-13 = m

16 = x

y = -5

Solve.

1) 5x = 35

2)

3) 9 = -3m

4)

5 5x = 7

126

=−x

126

=−x

(-6)(-6)

-72 = x

-3 -3-3 = m

y÷ =−4 8× ×4 4

y =−32

Solving Equations Involving Fractions3

59x =Long Way Short Way

3

59x =

3

5

3

5

x = ÷935

x = •91

53

=45

3x =15

x = •91

53

=45

3

x =15

Easier to multiply by the reciprocal!

3

59x =

€

53 ⎛ ⎝

⎞ ⎠

€

53 ⎛ ⎝

⎞ ⎠

Solve.

1) 7x = 16

2)

3) 9 = -m

4)

7 7

k

−=−

28

k

−=−

28 (-2)(-2)

k = 16

(-1)9 = -m(-1)

-9 = mx = =167

227

−=

y

47

−=

y

47(-4) (-4)

y =−28

Solve.1)

2)

3)

4)

2

714y =

€

72 ⎛ ⎝

⎞ ⎠

€

72 ⎛ ⎝

⎞ ⎠

y = •141

72

x =49−

=2

318m

€

−32

⎛ ⎝

⎞ ⎠

€

−32

⎛ ⎝

⎞ ⎠

y = •−18

132

x =−27

162

7= x

−=

4

59m

€ 72 ⎛ ⎝

⎞ ⎠

€

72 ⎛ ⎝

⎞ ⎠

7

2

16

1• =x

56 =x

€

−54

⎛ ⎝

⎞ ⎠

€

−54

⎛ ⎝

⎞ ⎠

m = •−9

154

m =−

=−454

1115

Acceptable Answers

-4k = 14-4 -4

k =−144

k = − 72

= − 35.= − 31

2

There is nothing improper about an improper fraction!

All answers must be fully reduced!