Whatever you do in life, it is a fact that mathematics is inescapable. Whatever be your field of work, in the future, mathematics and especially algebra will help you out. In your basic course, you will come across two main concepts, when you are solving problems, which are 'Equation' and 'Expression'. Here, we aim to explain their difference.
How Does an Equation Differ From an Expression, in Algebra?
A variable is an unknown quantity that needs to be determined through calculation. The most celebrated alphabet used for this purpose is 'x' but any other could be used as well. A variable is a useful concept that helps you in formulating a mathematical problem.
An expression and an equation are formed out of combination of variables and establishing of relations between them, using mathematical operators (+, -, x, etc.).
It is just a string of variables and numbers, connected together by mathematical operators. An expression cannot give you a solution. You can simplify an expression but not solve it.
The example 'x + 3' is an expression, as it only says 'three more than a number'. On the other hand, 'x + 3 = 0' is an equation as it says 'three plus a number equals to zero'.
First example is an expression, as it does not enable you to calculate the value of x, while the second example is indeed an equation, as it helps you solve for the value of the unknown variable 'x'. (If you solve it, you will discover that x = -3).
If you have a problem with one unknown, you need one equation to solve it. A problem with two unknowns will require two equations for solution of both variables. So as a rule, you need as many equations to solve a problem, as there are variables. An equation always has a sign '=' that denotes equality, while an expression doesn't have one.
An expression is an indefinite idea expressed in mathematical language, while an equation is a definite relation between quantities. Expressions come together to form an equation and the solution of problem is almost always guaranteed, once you set it up.
Most of the basic algebra is just setting up the right equations to find a solution to a problem. To get better at algebra, there is no substitute for practice. Just like any other language; as you become more fluent in the mathematical language, expressing your problem in equations, will become simpler.