More complex equation solving

Today we looked at some more complex equations and how we solve these. The worksheet we looked at can be found in the "Worksheets" tab.

These problems have pro-numerals on both sides of the equals sign in the equations. We want to get rid of the pro-numerals on one side of this equation. For example:

4x - 7 = 2x + 1

The first thing we want to do with these is to get rid of the '2x' on the right hand side of the equation. We do know how to do this from previous examples. We want to subtract 2x, remembering to do this to both sides of our equation. We the get:

4x - 7 - 2x = 2x + 1 - 2x

Doing these sums (by collecting like terms) we get:

2x - 7 = 1

We can now solve this like we would have with our previous examples.

2x - 7 + 7 = 1 + 7
2x = 8
2x ÷ 2 = 8 ÷ 2
x = 4

So the techniques we use are very similar to what we have previously done, however there is the extra step at the beginning where we remove the pro-numeral from one side of the equation.

Another example could be:

2(2x + 4) = 3(6 - 2x)

The first step with these is to expand the equation. This then gets us:
4x + 8 = 18 - 6x

Next, we want to get rid of the "-6x" term from the right hand side of the equation by adding 6x, again remembering to do this to both sides of our equation. We then get:

4x + 8 + 6x = 18 - 6x + 6x
10x + 8 = 18

Now we can solve it

10x + 8 - 8 = 18 - 8
10x = 10
10x ÷ 10 = 10 ÷ 10
x = 1

Finally, we may get examples like these:

a/3 + a/4 = 7

To solve these, we want to get rid of the fractions. To get rid of the first fraction, we first want to multiply everything by 3 (i.e. the denominator of this first term). We get:

a/3 x 3 + a/4 x 3 = 7 x 3
a + 3a/4 = 21

Now that we have got rid of one of the fractions, we want to get rid of the other one. To do this we again will do the same, multiply everything by 4 (the denominator of the second term). We then get:

a x 4 + 3a/4 x 4 = 21 x 4
4a + 3a = 84
7a = 84

We can then solve this easily. We get:

7a ÷ 7 = 84 ÷ 7
a = 12


Using these new skills we should be able to work through the whole worksheet. There are a lot of questions, so I have cut a few out. I only want you to do the following questions:
Question 1 - a, b, d, e, g, h
Question 2 - a, b, c
Question 3 - a, c, e
Question 4 - a, c
Question 5 - a, d

As always, if you have any questions feel free to comment on this post, or email or chat to me in person.