ALGEBRA!!!
“X = ?”
Solve for each X using LOGIC or ALGEBRA:
1)
2)
3)
4)
5)
6)
7)
8)
X+5=8
2X = 20
X + X + X + X = 40
100 + X = 200
X2 = 100
50X + 20X = 70
50X + 20X = 140
100  25
X
9) 100X2= 400
10) 100 – X = 57.2
BONUS: X 10
ANSWERS:
1) 3
2) 10
3) 10
4) 100
5) 10
6) 1
7) 2
8) 4
9) 2
10) 42.8
Bonus = 100
How to move #’s to the other side of the equation.
(across the = sign)
Always SWITCH OPERATIONS as you cross = .
This means:
+- +
X÷
÷X
2
Ex: You are 2 years younger than your brother.
U + 2 = B This is the same as:
U = B – 2 See the 2 went from +  -
Ex: 5x = 20 Here x = 4
vs. x = 20 Here x = 4 again.
5
Try the same questions applying algebra rules:
1) X + 5 = 8
X=8–5
Any time you make a move, SIMPLIFY!
X=3
Once x is by itself you have the answer.
Aka “ISOLATE THE VARIABLE”!
Proofs are easy!
Always plug your answer back into the
original equation and make sure it works
perfectly.
2) 2X = 20
X = 20
2
X = 10
3) X + X + X + X = 40
4X = 40 Combine any common terms 1st!
X = 40
4
X = 10
4) 100 + X = 200
X = 200 – 100
X = 100
5) X2 = 100
X = 100
X = 10
6) 50X + 20X = 70
70X = 70
X = 70
70
X=1
7) 50X + 20X = 140
70X = 140
X = 140
70
X=2
8) 100  25
X
You absolutely need x on top to solve!!
Don’t bother isolating x if it is on the bottom
of a fraction!!
This time we will NOT move the 100.
We will move the X 1st!!
100 = 25X
Now move the 25 to get x by itself.
100  X
25
4=X
9) 100X2= 400
X2 = 400
100
X2 = 4
X= 4
X=2
Proof:
100 (2)2 = 400 ?
100 (4) = 400 √
10) 100 – X = 57.2
- X = 57.2 – 100
- X = - 42.8
You cannot have a – x in your final answer!
X must be positive!
X =  42.8
1
X = 42.8
OR, if you really know your math, you are
technically allowed to go through a whole
equation and switch every +/- sign!
This is actually what we did above anyway in our
last 3 lines…
- X = - 42.8
X = 42.8
OR
10) 100 – X = 57.2 Alternate method.
This time move the x instead of the 100.
Move the x so it will become +!
We are not always isolating x 1st!
100 = 57.2 + X
Then move the # away from x.
100 – 57.2 = X
42.8 = X
In algebra…
Note: Do not switch the +/- as you cross = !
Only switch operations!
Assignment
Solve using algebra:
1) 2x + 3x + 4x = 90
2) 4x – 2x + x = 60
3) 100 + x = 2x
***Combine all x’s on one side (either
side) of = first!! Here I would definitely
choose the RIGHT side for the x’s!! This
will keep my x’s positive 
4) 100 + x2 = 500
5) 10x  4  5
6)
100  20  70
x
7) Do a proof for each of the above.
Show at least 3 on paper.
Answers
1) 10
2) 20
3) 100
4) 20
5) 90
6) 2
Algebra and Word Problems (worksheet #1):
#1-32
Do both sides of the page – all questions!
Do proofs to check your answers.
Algebra with Fractions (worksheet #2):
See worksheet #1-77
Check answer key.
Algebra & Factoring
Ex:
x2+7x+12=0
(x+3)(x+4)=0
x=-3 and x=-4
Do a proof and you will see that there are two
possibilities for x in this question. Both -3 and
-4 work!
Ex:
x2+x-20=0
(x+5)(x-4)=0
X=-5 and 4 or you could say x=-5,4
Ex:
x2-5x+6=0
(x-3)(x-2)=0
X=3,2
Ex:
(x+5)(x-2)(x-3)(x+1)x=0
*If the equation is already in factored form
then you can see the answers for x instantly.
*In this question there are 5 factors, each
containing an x so there will be 5 answers!
X=-5,2,3,-1 and 0!
Sample proof if x=0
(0+5)(0-2)(0-3)(0+1)0=0??
(5)(-2)(-3)(1)(0)=0 Yes, this is true so 0 works.
So do all the other numbers shown.
*Our shortcut to answers only work however
if the equation is =0 to begin with.
If it isn’t, rearrange it, and make it =0 before
you begin…
*In general think how do I make each term or
bracket = 0??
Ex:
X(5+X)= 0
X=0,-5
Proofs:
If x = 0
0(5+0)=?0
0(5)=0√
If x=-5
-5(5+-5)=?0
-5(0)=0√
Ex:
X2+7X=0
X(X+7)=0
X=0,-7
Ex:
7X+14=0
7(X+2)=0
X=-2 only!
(Note: x≠0)
Assignment:
1. x(x+5)(x-2)=0
2. x2+29x+100=0
3. x2+40x+400=0
4. x2-13x+40=0
5. x2-2x=-1
6. x2-25=0
7. x2=49
Answers:
1. 0,-5,2
2. (x+25)(x+4)=0 x=-25,-4
3. (x+20)(x+20)=0aka(x+20)2=0x=-20
4. (x-8)(x-5)=0x=8,5
5. x2-2x+1=0(x-1)(x-1)=0 or (x-1)2 x=1
6. (x+5)(x-5)=0x=5,-5 or x=±5
7. X2-49=0(x+7)(x-7)=0x=±7
OR
X2=49 so x=√49 x=±7
Algebra Review
1. 4x + 8 = 20
2. 4x = 20 + 3x
3. 4x = 20 + 5x
4. 4x  20
5.
20 1 11
x
6. –x+5+2x-4=101-x
7. 5x 1  2
x 1   3
4
2
9. 3  2x  x 2 2
10. 13 x  13  x 1
11. x 41  x 21
8.
1
1
7
2
3
3
12. 𝑥 + =
13. Which of the steps are correct as a
first step in the following question?
2( x  2) 1  7
4x
4
Write correct or incorrect by each
option.
For each correct first step, complete the
rest of the question.
a) ( 2(x4x 2) 1 74 )4
b) ( 2(x4x 2) 1 74 )4x
2( x  2)  7 1
4x
4
d) 2(x4x 2)  74 1
e) 2(x  2) 1 7(44x)
f) 2x4x 4  4x  74
4x
c)
14. 2(3-a)=3(a-3) and show a proof!
15.Solve the systems for BOTH variables:
a) 2𝑥 = 5𝑦 − 8
2𝑥 − 2𝑦 = −2
b) 𝑥 + 𝑦 = 10
5𝑥 − 2𝑦 = 1
c)
1
2
𝑥 + 3𝑦 = 14
𝑥 + 2𝑦 = 12
Answers:
1)x=3
2)x=20
3)x=-20
4)x=80
5)x=2
6)x=50
7)x=-5
8)x=-5
9)x=2
10)x=2
11)x=3
12)x=4
13)b,c,f x=4
14)a=3
Proof:
2(3-3)=?3(3-3)
2(0)=3(0)
0=0√
15) a) 1,2
b) 3,7
TEST to follow…!
c) 4,4