Solving Equations


You will get asked to solve equations in your exam.  Below are the types of equations you should study if your aiming for a C in maths.  Equations can crop up on either your calculator or non calculator paper but they will probably turn up on both!

Example Question

Solve:

a) 3(2x - 4) = 18
b) 2x + 14 = 2(2x - 3)


Solution

a)
To solve equations we want to find the value of x.  In other words we want x on its own the left hand side of the equation.  To achieve this we need to use inverse operations.

3(2x - 4) = 18
First expand the brackets to get:
6x - 12 = 18
Now to get rid of "-12" we add 12 to both sides which gives:
6x = 30
Finally remember "6x" means "6 times by x" so we divide both sides by 6:
x = 30 6
x = 5

b)
Here we have a slightly harder example but the basic method stays the same.

2x + 14 = 2(2x - 3)
First expand the brackets to get:
2x + 14 = 4x - 6
Now since we have x terms on both sides of the equation we write the equation with the larger x term on the left:
4x - 6 = 2x + 14
Now we get rid of the smaller 2x term by subtracting 2x from both sides:
2x - 6 = 14
Now add 6 to both sides:
2x = 20
Finally divide both sides by 2 gives:
x = 10

Test Yourself!
Grade
G/F Solve:     a + 2 = 10 a =
G/F Solve:     3b = 45 b =
E/D Solve:     2c - 4 = 18 c =
D Solve:     4(d + 2) = 10 d =
D/C Solve:     5(e - 2) = 3e e =
D/C Solve:     5f - 1 = 6 + 3f f =
C Solve:     7(g - 2) = 2(2g + 5) g =
C Solve:     5(h + 2) = 12 + h h =


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