Guide to Math

Algebra 102:

Now that you know you can do the same operation (e.g. +2) to both sides, and it still remains true, remember when we are solving for x, x is some unknown number, but it is still a number!

So if you can add 2 to both sides to keep it true, you can do the same with 2x. You needed to know that to solve question e) in the previous part (or you needed to know how to multiply by -1).

You can always treat x like a number when you are solving an equation. By that I mean in the same sense as +2x to both sides, not just putting in a random number where x was.

Here is an example to help you understand:

x + 5 = 2x

Subtract both sides by x

x - x + 5 = 2x - x, and the two 'x's cancel out, because x - x = 0

5 = 2x - x, and if you treat x like a number, 2 times a number subtract that number gives you the same number! 2 - 1 = 1, 4 - 2 = 2, 6 - 3 = 3, so therefore, 2x - x = x.

5 = x :)

So now you have the basics of algebra! Here is a few- okay maybe more than a few- questions for you to solve: Have fun! Remember: you cannot ÷ 0 !

a) x + 5 = 8

b) x - 2 = 4

c) x - 14 = 9

d) x + 7 = 8

e) x × 7 = 7

f) 5 × x = 10

g) 2x + 5 = 11

h) 3x - 9 = 3

i) 11 - x = 9

j) 5 + 5x = 25 + 10

k) 8 + x = 8

l) 18 = 2x + 12

m) 24 ÷ 3x = 8

n) x = x + 1

o) 3x = x + 1 + 2 + 3 + 4

p) 5x ÷ x = 5 - x

q) 9x - 8x + 7x - 6x = 5 - 4 + 3 - 2

r) 2x ÷ 5 = 10

s) 2x + 4 = 10 - x

t) 3x ÷ 5 = 2x - 7

u) 3x + 5 - 2x + 5 = 30 - 4x

v) 9x ÷ x = 7 + x

w) 2x + 7 = 9

x) 7x ÷ 5 = 32 - 5x

y) 9x - 5 = 13

z) 25x ÷ 5 = 10

And there you have it, check your answers on the next page, and if you got them all, well done! Watch out for some trick questions!