1. Solving Equations Finding Your Balance

2. Balance Remember that the Equal Sign Means Balance
The equations are the same on both sides.
2+4=6
6=6

3. How to solve an Equation
To solve for a variable you have to remember TWO things.
1) Try to Isolate the Variable
(Isolate means get the variable by itself.)
2) What ever you do on one side of the equation, you have to do the same to the other side.

4. Example (Write this down!)
Begin to isolate the variable x by completing the INVERSE OPERATION of 3
4x + 3 – 3 = 19 – 3
4x = 16
Simplify
Inverse Operation of multiply is Divide. Divide both sides by 4
Simplify
Solved!
X = 4

5. Now Check! Substitute 4 every place you see an X 4(4) + 3 = 19
Solve using PEMDAS
= 19
19 = 19
True! It must be correct!

6. Try one
S = 21
S + 7 – 7 = 21 – 7 Isolate the Variable by doing the inverse operation to BOTH SIDES
S = 14 Simplify. Solved!
= 21 Check
21 = 21 Correct!

7. Harder One 3m – 2 = 7 3m – 2 + 2 = 7 + 2 3m = 9 3m/3 = 9/3 m = 3
Add the inverse to Isolate the Variable.
Simplify
Divide by 3 (inverse of Multiply)
Solve!
Check on your own.

8. Even Harder 45 = 5x + 35 45 – 35 = 5x +35 – 35 10 = 5x 10/5= 5x/5
Check
45 = 5(2) + 35
45 =
45 = 45

9. Division Isolate the Variable by subtracting 2 from each side.
Inverse of Division is Multiplication. Multiply each side by the Denominator.
Simplify
Solved!

10. Variables on BOTH SIDES!
5x - 6 = x
Eliminate the 6 by adding 6 to both sides
Simplify
Eliminate (-x) by adding x to both sides
Divide both sides by 6
Solved!
Now check.
5x – = – x
5x = -6 – x
5x + x = -6 –x + x
6x = -6
6x/6 = -6/6
x = -1

11. Check 5x - 6 = - 12 - x 5(-1)- 6 = -12 – (-1) -5 – 6 = -12 + 1
Substitute
Simplify
It Checks!
5(-1)- 6 = -12 – (-1)
-5 – 6 =
-11 = -11

12. Practice Problems 2.) 4x + 6 = - 22 1.) 7x + 4 = 88 4.) 7x + 5 = 75

13. Practice Combine Like Terms then Solve
1) 6x x = 9
2) 3x x = - 119
3) x x = 11
4) - 8 = x - 3x - 2
X = 1
X = -12
X = 2
X = 3