Solving Problems With Linear Equations

Solving Problems With Linear Equations-37
We are left with one parenthesis, that is multiplied by 6. Since we have nested parenthesis (one within another), we are going to start removing them.The first parenthesis (the exterior one) is multiplied by –2.

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.

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.

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.We are going to multiply everything by the least common multiple of the denominators, which is 6.Be careful with the parenthesis: We resolve the equation: We have 0 = -2 which is a false mathematical equality.We can see this by going to the linear equations problems section.These equations are known as linear, because the monomial literal part does not have an exponent (for example, \(3x\) can be part of a linear equation, but \(3x^2\) cannot because it is quadratic), so represented in a chart appears as a straight line.In this equation, we have a nested parenthesis (parenthesis within a parenthesis) and it is multiplied by fractions.But before we worry about this, we will multiply all the equation by the least common multiple of the denominators, 6: Now we are going to the parentheses: on the left there are two, but we will treat it like one.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.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.


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