Hard Algebraic Equations

Solving equations

An equation is almost a sort of seesaw: you add something to the left, lose the balance and are forced to do the same to the right; you divide and multiply by something, once again, the same must be done to the other side; if you subtract something, there is no exception. Therefore, solving equation means, getting rid of everything around x by seesaw method.

E.g.1

2(x + 5) = 18
:- 2 => 2(x + 5) :- 2 = 18 :- 2
x + 5 = 9
- 5 => x + 5 - 5 = 9 - 5
x = 4

E.g.2

5(x - 2) = 2(x - 3)
5x - 10 = 2x - 6
+10 => 5x - 10 + 10 = 2x - 6 + 10
5x = 2x + 4
-2x => 5x - 2x = 2x - 2x + 4
3x = 4
:-3 => 3x / 3 = 4 /3
x = 1.3

E.g.3

4(x + 4) + 3(x -3) = 2(x -3) + 12
4x + 16 + 3x - 9 = 2x - 6 + 12
7x + 7 = 2x + 6
- 7 => 7x + 7 - 7 = 2x + 6 - 7
7x = 2x - 1
-2x => 7x - 2x = 2x - 2x -1
5x = -1
:-5 => 5x / 5 = -1 / 5
x = -0.2

E.g.4

(x + 5) / 4 = (x -3) / 2
X 4 => 4 X (x + 5) /4 = 4 X (x- 3) / 2
(x + 5) = 2 (x -3)
x + 5 = 2x - 6
- 5 => x +5 -5 = 2x - 6 - 5
x = 2x - 11
-2x => x - 2x = 2x - 2x -11
-x = -11
-1 X x = 11

E.g.5

3 + 2(x + 5) = 3 - (2x - 1)
3 + 2x + 10 = 3 -2x + 1
13 + 2x = 4 - 2x
-13 => 2x + 13 - 13 = 4 - 2x - 13
2x = -2x - 9
+2x => 2x + 2x = 2x - 2x - 9
4x = -9
:- 4 => 4x / 4 = -9 / 4
x = -2.25

Practice is the key to mastering maths; please visit this page, for more worksheets.

Now, in order to complement what you have just learnt, work out the following questions:

1. 2(x + 9) + 3 = 13
2. 3(x + 9) - 6 = 19
3. 3(x - 2) = 2(x - 4) + 7
4. 5(x - 3) + 2(x + 1) = 2(x - 2)
5. 4(x - 2) - 2(x - 1) = 3x + 16
6. 2x + 4(2x - 1) = 4(x + 2)
7. 3(x + 3) - 2(x + 1) = 2(x -1) + 4x
8. 2 - 3(x + 1) = 2(2x -3)
9. 4(x -3) - 3(x + 2) = 5 + 2(x + 2)
10. 3 - (x-3) = 4 + (x - 2)

Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
This is also an opportunity to pay tribute to the intellectual giants like Newton, Pythagoras and Leibniz, who came up with lots of concepts in maths that we take for granted today - by using them to serve mankind.

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Recommended Reading

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