Ch 2.4 (part 1)

Two Step

Objective:

To solve two-step variable equations using both the Inverse Property of Addition

& the Inverse Property of Multiplication

Definition

Two Step Equation Two operations are performed: Inverse Property of Addition Inverse Property of Multiplication

The operations are performed in REVERSE ORDER from the Order of Operations

GOAL: Isolate the variable expression then Isolate the variable

1) Use Inverse Property of Addition. (Undo addition with subtraction. Undo subtraction with addition.)

2) Use Inverse Property of Multiplication.(Hint: Multiply by the reciprocal for fractions)

Perform both operations to both sides of the equation

Rules

Example 1

4m + 2 = 10

-2 -24m = 8

4 4

m = 2

Use Inverse Property of Addition

Use Inverse Property of Multiplication

Example 2

Use Inverse Property of Multiplication

Use Inverse Property of Addition

€

−2 =x −1

6

+ 1 +1

€

−12 = x −1

(6) (6)

-11 = x

Example 3

5x + 2 = 37-2 -2

5x = 355 5

x = 7 €

7 =2

5x + 3

-3 -3

€

4 =2

5x

10 = x

-2x - 7 = 3+7 +7

-2x = 10-2 -2

x = -5

€

5

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

5

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

−2 = 2 +x

4-2 -2

€

−4 =x

4

-16 = x

€

4( )

€

4( )

Example 4

Example 5

Example 6

Solve.

1) -9x + 1 = -80 -1 -1

-9x = -81-9 -9

x = 9 €

8 +x

−4= 53)

-8 -8

€

x

−4= −3

x = 12

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

9x = 09 9

x = 0

€

−4( )

€

−4( )

€

−6 +x

4= −54)

+6 +6

€

x

4=1

x = 4

€

4( )

€

4( )

5) 5x + 4 = 39 7) 7 - x = 12

6) 8)x

34 2− = 13 6

5= −

x

-4 -45x = 355 5x = 7

+4 +4x

36=(3) (3)

x = 18

-7 -7- x = 5

(- x) = 5(-1) (-1)

x = -5

-6 -6

75

=−x

(-5) (-5)

-35 = x

Solve.

9) 11)

10) 12)

103

428− =x

-10 -10

− =3

418x

€

−43

⎛ ⎝

⎞ ⎠

€

−43

⎛ ⎝

⎞ ⎠

€

−34

x ⎛ ⎝

⎞ ⎠

x = -245

64 11x− =

+4 +45

615x =

€

65 ⎛ ⎝

⎞ ⎠

€

65 ⎛ ⎝

⎞ ⎠

x = 18

−+ =

2

39 21x

-9 -9

−=

2

312x €

−32 ⎛ ⎝

⎞ ⎠ €

−32 ⎛ ⎝

⎞ ⎠

x = -18

293

45= +x

-5 -5

243

4= x €

43 ⎛ ⎝

⎞ ⎠ €

43 ⎛ ⎝

⎞ ⎠

32 = x

Solve.