-3 - 3

Objective - To solve equations with the variable in both sides.

Solve.2x + 4 = 5x - 17

2x + 4 = 5x - 17 2x + 4 = 5x - 17-2x -2x

4 = 3x - 17+17 +17

21 = 3x3 3

7 = x

-5x -5x-3x + 4 = -17

-4 -4

-3x = -21

x = 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.

4) Easiest to undo add/subtract before multiply/divide.

1) Goal: Isolate the variable on one side of the equation.

4) Easiest to undo add/subtract before multiply/divide.

2) Undo operations with their opposite operation.

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

Solve.1) 4(x - 2) - 2x = 5(x - 3)

4x - 8 - 2x = 5x - 152x - 8 = 5x - 15

-2x -2x

-8 = 3x - 15+15 +15

7 = 3x3 3

x 7

32

1

3

2) 3(x + 2) - (2x - 4) = - (4x + 1)3x + 6 - 2x + 4 = - 4x - 1

x + 10 = - 4x - 1+ 4x + 4x

5x + 10 = -1- 10 -10

5x = -115 5

x = =11

5 2

1

5

3) 5(m - 6) = 10 - 4[2(m - 7) - 5m]

5m - 30 = 10 - 4[2m - 14 - 5m]

5m - 30 = 10 - 4[-3m - 14]

5m - 30 = 10 + 12m + 56

5m - 30 = 12m + 66-5m -5m

-30 = 7m + 66-66 -66-96 = 7m7 7

m 96

713

5

7

Solve each equation below.a) 3x - 5 = 2x + 12 b) 3x + 8 = 2(x + 4) + x

c) 3x + 2 = 2(x - 1) + x

-2x -2xx - 5 = 12

+5 +5x = 17

3x + 8 = 2x + 8 + x3x + 8 = 3x + 8

-3x -3x

8 = 8

3x + 2 = 2x - 2 + x3x + 2 = 3x - 2

-3x -3x

2 = -2

One Solution Identityx = any real number

True !

False ! No Solution

Solve.4) 4(y - 2) + 6y = 7(y - 8) - 3(10 - y)

4y - 8 + 6y = 7y - 56 - 30 + 3y 10y - 8 = 10y - 86

-10y -10y

-8 = -86False Statement

No Solution

Solve.5) 3(4 + k) - 2(3k + 4) = 5(k - 3) - (8k - 19)

12 + 3k - 6k - 8 = 5k - 15 - 8k + 19 -3k + 4 = -3k + 4+3k +3k

4 = 4True Statement

Infinitely Many Solutions

x = any real number

Use a variable equation to solve.4) Find a number that is 20 more than 4 times its opposite.

Let x = the number -x = the opposite

x = 4(-x) + 20x = -4x + 20

+4x +4x

5x = 205 5x = 4