Solving Problems With Linear Equations

For example, the equation \(x = x 1\) (which means a number equals the consecutive number) does not have a solution, because this is never true.Actually, this equation is reduced to 1 = 0, which is impossible.

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In mathematics, linear equations are the introduction to algebra.

Their understanding is vital for any kind of equations: quadratic equations or bigger, exponentials, irrational, etc. In real life, although it may not be though of straight away, but equations are a very useful tool that allows us to resolve problems that we face on a day to day basis.

We will multiply all the content of the exterior by –2.

At the same time, on the right, we multiply all the content by 9.

To remove it, we multiply all the content of the parenthesis by -2: Now, the parenthesis on the exterior is multiplied by 6.

To remove it we multiply the content by 6: Finally, the parenthesis that is left is multiplied by –12, so to remove it we multiply the content by –12: Now we are going to remove the fractions, but before this, we add some of the elements we have to reduce the length of.When all is said and done, a word problem, stripped from inessential details, translates into one or more mathematical equations of one kind or another.After the equations have been solved, the result can be translated back into the ordinary language. Mathematical formulation contains only what is important in a problem.This means that whatever the value of x, the equations is always going to be true. To be solved, a word problem must be translated into the language of mathematics, where we use symbols for numbers - known or unknown, and for mathematical operations.But how does one know what is important and what is not, what is essential and what can be dispensed with?One simple approach to find out is to try changing the problem a small piece at a time.This fact assures us that if there is a solution, there can only be one solution (except in special cases where there are infinite solutions).We say if there is a solution because sometimes equations don not any solution.What is adding on one side will change to the other side subtracting and vice versa.Afterwards, we put the x's to one side of the equality and the numbers to the other. First, we remove the parenthesis: since it has a negative sign in front of it, we change the sign of all the elements in the inside.


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