Solving Equations: a strategy

The mathematics behind solving equations is basic.

The hardest part:

What do I do first?…

THE GREAT SOLVING EQUATIONS PLAN!!!

The following plan will allow you to solve any equation you come across in five easy steps…

Step 1:Eliminate any denominators

using the LCD technique.

Step 2:Eliminate any brackets using the

Distributive Law.

Brackets lock terms together……that’s bad!

Step 3:Collect like terms on each side

of the equation.

Remember the sign in front of the term stays with the term.

Step 4:Isolate the variable.

Eliminate the smaller variable if they are on both sides.

Step 5:Solve the 2 step equation.Add/sub first, then mult/divide.

Solve the following equations:

1. 4x = 204 4

1

1x = 5

2. 7 + 3y = 34

3 3

1

1y = 9

-7 -7

3y = 27

Check this answer

Check

7 + 3(9) = 34 ?

7 + 27 = 34

34 = 34 YES!!!

3. 3z + 4 = 8z - 21

-5 -5

1

1

-5z = - 25

-8z -8z

-5z + 4 = -21-4 -4

z = 5

Check this answer

Check

3(5) + 4 = 8(5) – 21 ?

15 + 4 = 40 – 21 ?

19 = 19 YES!!!

4. 2(x + 3) = 10

2 2

1

1x = 2

-6 -6

2x = 4

2x + 6 = 10

Check this answer

Check

2(2 + 3) = 10 ?

2(5) = 10

10 = 10 YES!!!

5. 3 + 4(x – 2) = 6x + 7 – 1x

-1 -1

1

1

-1x = 12

-5x -5x

-1x – 5 = +7

4x - 5 = 5x + 7

3 + 4x – 8 = 6x + 7 – 1x

+5 + 5

x = - 12

6. 4

3d = 12

4

3d = 12 X 33 X

1

14d = 364 4

1

1d = 9

HomeworkRe-attempt various problems.