Question

Solve: 2x – 3 = 9 and verify the solution.

Answer 1

Hint: Consider the linear equation then make the variables as subjects or take variables to one side and constant term to the other and hence find the value of variable ‘x’. After that put the value of x in the left hand side of the equation and check its value is equal to the other side.

Complete step-by-step answer:
First we will understand what are linear equations and learn some facts about them.
Let a linear equation can be written in form of,
\[ax+b=0\]
Where a and b are real numbers and x is a variable. This form is sometimes called the standard form of linear equations. Please note that most linear equations will not start of this form. Also the variable may or may not be an x or please don’t get too locked into always seeing x there.
Now for solving linear equations we will make heavy use of facts which are,
(i) If a = b then a + c = b + c for any value of c. All this saying is that we can add a number c to both the sides of the equation and not change the equation.
(ii) If a = b then a – c = b – c for any value of c. All this saying is that we can subtract a number c to both the sides of the equation and not change the equation.
(iii) If a = b then ac = bc for any non-zero value of c, so that the value of the equation remains unaltered.
(iv) If a = b, then \[\dfrac{a}{c}=\dfrac{b}{c}\] for any non – zero value of c, so that the value of the equation remains unaltered.
These points are very important and help very much while solving any linear type of equations they should be kept in mind.
So, the given linear equation is:
2x – 3 = 9
Now we will add 3 to both the sides we get,
2x – 3 + 3 = 9 + 3
Or, 2x = 12
So, the value of x is 6.
Now for verification we will take the value of x which we got and put it on the left and right side. If they are the same then we can say it is correct and verified.
So, on the left hand side it is given 2x – 3 hence on putting x as 6 we get \[2\times 6-3\] or 12 – 3 or 9 which is equal to the right hand side of the equation.
Hence the solution of x is verified.

Note: Students while solving large linear equations tend to make calculation mistakes so they should be careful about every step or calculation while doing it. For verification too they should be careful.