1. Algebra 2
Miss Hudson’s Maths

2. To strip terms away - do the opposite!
Solving Equations
The aim is to find the value of the variable that makes the mathematical sentence true.
To do this we need to step by step strip all other terms away from the variable (usually x) ie isolate the x
What you do to one side, you do to the other in order to keep the sides balanced. x 7 = 3
eg 1:
x 7
6x = 18
eg 3:
x 7 6 6
x = 21
x = 3
+ 4
+ 4
eg 2:
x - 4 = 7
To strip terms away - do the opposite!
x = 11
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3. eg 5: (gives a negative answer) eg 6: (gives a fractional answer)
+ 5
+ 5
eg 4:
2x - 5 = 3
2x = 8 2 2
x = 4
eg 5: (gives a negative answer)
eg 6: (gives a fractional answer)
-15
-15 -1 -1
6x + 1 = 9
2x + 15 = 1
2x =
-14
6x = 8 2 2 6 6 4
or 1 1 3
x = -7
x = 3
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4. x eg 7: - 4 = - 3 3 x = 1 3 x = 3 2 x - 4 eg 8: = -2 3 2 x - 4 = -6+4 +4
eg 7:
- 4 = - 3 3
x 3 x
x 3
= 1 3
x = 3
x 3
2 x - 4
x 3
eg 8:
= -2 3
+ 4
+ 4
2 x - 4 = -6
2 x = - 2 2 2
x = - 1
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5. Equations with Brackets
eg 9: ( 2 y - 1 ) = 21
Expand the brackets first; so we go 3 x 2y and 3 x -1 =
+ 3
+ 3
6 y - 3 = 21
6 y = 24 6 6
y = 4
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6. Collect the numbers on the other side
If x appears on both sides of the equation we need to collect all the x’s on the side that has most of them first.
-3x
-3x
eg 10: x = 3x + 8
2x = 8 2 2
Collect the numbers on the other side
x = 4
+ 4x
+ 4x
eg 11:
-4x + 8 = 2x - 20
+ 20
+ 20
8 = 6x
- 20
28 = 6x 6 6 4⅔ = x
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7. Writing Equations & Solving Them
eg 1: I am thinking of a number. If I multiply this number by 3, I get a result of What is the number?
Solution:
Let the number be x
3x = 18 3 3
x = 6
The number is 6
eg 2: When 4 times a number is added to 5 the result is Find the original number by forming an equation and solving it.
Solution:
Let the number be n -5 -5
4n + 5 = 17
4n = 12 4 4
n = 3
The number is 3
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8. eg 3: Twice a certain number is 7 more than the number.
What is the number?
Solution:
Let the number be x -x -x
2x = x + 7
x = 7
The number is 7
eg 4: When 3 times a number is added to the original number
the result is 16. Find the original number by forming an
equation and solving it.
Solution:
Let the number be n
3n + n = 16
4n = 16 4 4
n = 4
The number is 4
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9. Write an algebraic expression for each of the following statements
Eight is added to the number n.
Six is added to three times the number n.
Four is added to five times a certain number x.
Thirty is subtracted from six times a certain number y.
A certain number m is multiplied by negative five and then eight is added.
A certain number q is divided by four and then six is added.
Twelve is divided by negative x.
The number x is multiplied by negative three and the result is divided by five.
Four times the number z is subtracted from negative three.
Three times the number y is divided into negative twelve.
Write an algebraic expression for each of the following statements
Miss Hudson’s Maths