An equation may contain some x-terms and some numbers. We want to manipulate the equation to isolate a single x term on one side and a number on the other side i.e x=some number. The last two sections showed that correct algebraic manipulation maintains balance between the left hand side (LHS) and right hands, and these rules were determined:

You can add a quantity on the LHS so long as you add the same quantity to the RHS

You can subtract a quantity from the LHS so long as you add the same quantity to the RHS. Note that subtraction is really the addition of a negative number, this is no really seperate rule.

You can multiply all terms on both sides by a quantity.

You can divide all terms on both sides by a quantity. Note that since division is really multiplication by a fraction, this is not really a seperate rule.

The "Solution Interface" will let you perform algebraic operations to solve equations. You are advised to start with 2 steps problems. A solution with the least number of steps can be seem by pressing "Answer". The 3 step problem is slightly harder than the 2 step problem. The 4 step problem contains fractions, and you need to find a strategy to deal with the fractions: try a few times before see the solution after pressing "Answer".

Press for a

exercise

exercise

Solve for x by using the buttons:

Multiply all terms

Divide all terms

Both sides add number

Both sides add x

Press to see the answer and working out:

After enough practice on the "Solution Interface" you should be confident. To check your progress solve the equations below and check compare your working out with solution. You may think a 4 step problem is a lot, actually problems in science and engineer can involve several hundred steps. Equations that suggested the existence of anti-matter, the trajectory of rockets to reach outer space, and many other problems, have all been solved on paper. The aim of this website is to give you a deep and visual understanding of maths topics so that you can solve problems without the aid of a calculator or computer.

Solve the following equation:

x input

Numerator

Denominator

Numerator

Denominator

Check you answer and working out below:

Solve the following equation:

x input

Numerator

Denominator

Numerator

Denominator

Check you answer and working out below:

Solve the following equation:

x input

Numerator

Denominator

Numerator

Denominator

Check you answer and working out below:

The approach for solving an equation is to use correct algebraic steps so that one side of the equation contains only a single "x" and the other side contains a number. We have discussed algebra from first principles and focused on the solution of some relatively simple problems. I hope that you have understood the basis of algebra and also the importance of solving equations neatly and systematically on paper; you know have a very good base to understand more advanced algebra and applications of algebra.