Solving a linear equation in one variable

Solving a Linear equation in one variable

In the previous post, we had discussed the variables and making a mathematical model of a physical problem. In this post, we are going to discuss the solving method solving a linear equation in one variable.

Suppose we have an equation x+5=15
Following steps are useful in solving it. 

Step:    Make arrangements in the equation so that there left only the term containing the                             variable on the left side of the equation. To do it, we will have to remove 5 from the left side. But to maintain equality, we subtract 5 from both sides.

We have
                    x+5-5=15-5          (Subtract 5 from both sides)
                             x=10
Thus, x=10 is the answer for this problem x+5=15

Let's take one more example: Suppose we have an equation 3x-2=16 and we are supposed to solve it for x.  We can proceed as follows

We have $3x-2=16$
Adding 2 both sides, we get
               $3x-2+2=16+2$
                       $3x=18$
Dividing both sides by 3, we get
                      $x=\frac{18}{3}$
                      $x=6$

Let's take another example. 
$\frac{5x}{2}-3=7$
To solve it , we will proceed as
First of all, we will add 3 both sides, we get
$\frac{5x}{2}-3+3=7+3$
       $\frac{5x}{2}=10$
Now multiply both sides by 2, we get
       $5x=2\times 10=20$
Now divide both sides by 5, we get
       $x=\frac{20}{5}\\ x=4$

Now try these problems
1. $7x-2=12$
2.  $25x+5=55$
3  $0.3x+0.2=0.8$
4.  $\frac {2}{x}+3=7$