1. Using Algebra to Solve Equations

2. Lets review algebraic expressions
A # increased by 5
A # decreased by 5
A # divided by 5
A # multiplied by 5
Formula for the area of a rectangle
x + 5
x - 5 x 5
5 x lw

3. Solving Equations Algebraically

4. The only rules that you
need to know...
Rule #1 - ISOLATE the variable on one side of the equation
Rule #2 - whatever you do to one side, you do the EXACT same thing to the other

5. 3x + 10 = 19
Equation in words:
3 times a # increased by 10 is 19
X = 3

6. Isolate the Variable on one side of the equation
Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other
3x + 10 = 19
Isolate the variable means that only the x is on the left side
3x = 19
3x = 9
X = 3
-10
-10

7. Isolate the Variable on one side of the equation
Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other
5n - 2 = 348
5n = 348
5n = 350
n = 70 +2 +2

8. Isolate the Variable on one side of the equation
Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other
2n +3 = 4
2n = 4
2n = 1
N = 1/2 -3
- 3

9. 1. 7x - 7 = 42
2. 5x + 9 = 19
3. 5y + 8 = 9
4. 56x - 78 = -22
5. 50x + 50 = 150
Isolate the Variable on one side of the equation
Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other

10. 1. 7x - 7 = 42
2. 5x + 9 = 19
3. 5y + 8 = 9
4. 56x - 78 = -22
5. 50x + 50 = 150
x = 7
x = 2
y = 1/5
x = 1

11. Expanding 4(5+n) = 20 + 4n a(b+c) = ab + ac Same as (a x b) + (a x c)
Expanded form
4(5+n)
= n

12. State the following in expanded form
a) 5(x + 6)
b) 7(5 + e)
= 5x + 30
= e
a(b+c)
= ab + ac
Same as (a x b) + (a x c)

13. One Last Important Concept: Combining Like Terms

14. As long as the variable is EXACTLY the same letter, they can be combined
If the variables are the same, they are referred to as LIKE TERMS
6x + 4x =
3n + n =
5n - n =
14a - 10a =
10x 4n 4n 4a

15. 14t - 4s -3x 12j - 4r 10n - 4n2 7x - 10x = 5j + 7j - 4r =
When we combine like terms, it is also referred to as simplifying
Simplify the following expressions:
4t + 10t =
6s - 10s =
7x - 10x =
5j + 7j - 4r =
3n – 4n2 + 7n =
14t
- 4s
-3x
12j - 4r
10n - 4n2

16. Steps to solving algebraic equations: Simplify (combine like terms)
4x + 6x = 100
10x = 100
x = 10
To double check our answer, substitute (10) into the original question:
4(10)+ 6(10) =
= 100
Steps to solving algebraic equations:
Simplify (combine like terms)
Isolate the Variable on one side of the equation
Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other

17. Steps to solving algebraic equations: Simplify (combine like terms)
4x - 12 = 3x
4x = 3x
x = 0
x = +12
To double check our answer, substitute () into the original question (left side and right side):
Left Side (LS): Right Side (RS):
4x x
= 4(12) = 3(12)
= = 36
= 36
-3x
-3x
Steps to solving algebraic equations:
Simplify (combine like terms)
Isolate the Variable on one side of the equation
Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other
+12
+ 12

18. Steps to solving algebraic equations: Simplify (combine like terms)
5x – 40 = 3x
5x = 3x
2x =
2x = 40
x = 20
Double check our answer
LS: RS:
5x x
= 5(20) = 3(20)
= = 60
= 60
-3x
-3x
Steps to solving algebraic equations:
Simplify (combine like terms)
Isolate the Variable on one side of the equation
Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other
+40
+ 40

19. -20 = -4x - 6x
Why is this a tricky question?
Subtract integers
Combining like terms
Isolate the variable