In previous topics of this unit we have learnt many basic concepts about linear equation in one variable. We know that a linear equation is that which when plotted on a graph sheet gives a straight line. A linear equation in one variable is a equation in which only one unknown quantity is present in the equation. Now in this topic we will learn about solving the linear equation in one variable.
Following steps must be followed while solving a linear equation in one variable:
Step I: Observe the linear equation carefully.
Step II: Carefully note the quantity you need to find out.
Step III: Divide the equation in two parts, i.e., L.H.S. and R.H.S.
Step IV: Figure out the terms containing constants and variables.
Step V: Transfer all the constants on the Right Hand Side (R.H.S) of the equation and variables on the Left Hand Side (L.H.S.) of the equation.
Step VI: Perform the algebraic operations on both sides of the equation to get the value of the variable.
Below are given few examples based on the above concept.
1. Solve: 2x – 4 = 48.
The given equation a linear equation in one variable with variable as ‘x’. So, we need to find out the value of ‘x’.
2x – 4 = 48
2x = 48 + 4
2x = 52
x = 52/2
x = 26.
Hence, the value of variable ‘x’ is 26.
2. Solve: 3x + 34 = 13 – 2x.
Both sides of the given equation contain unknown quantities. So, let us transfer all the unknown quantities at the L.H.S. and known quantities on R.H.S. So, the equation becomes:
3x + 2x = 13 – 34
5x = -17
x = -17/5
Hence, the value of variable ‘x’ is -17/5.
So, all the similar problems can be solved using above concepts.
Now there are another type of problems in linear equation in one variable.
These are word problems on linear equations in one variable.
Linear equation in one variable can be solved using following steps:
Step I: First of all read the given problem carefully and note down the given and required quantities separately.
Step II: Denote the unknown quantities as ‘x’, ‘y’, ‘z’, etc.
Step III: Then translate the problem into mathematical language or statement.
Step IV: Form the linear equation in one variable using the given conditions in the problem.
Step V: Solve the equation for the unknown quantity.
Now let us solve some problems based on above concepts:
1. The sum of two numbers is 36. The numbers are such that one of them is 5 times the other number. Find the numbers.
Let one of the numbers be ‘x’.
Then, 2nd number = 5x.
It is given that their sum is 36.
So, x + 5x = 36.
6x = 36.
x = 36/6.
x = 6.
Hence 1st number = 6.
2nd number = 5x = 5 x 6 = 30.
2. A father is 4 times older than his son. If sum of ages of both father and son is 50 years. Then find the age of both of them.
Let the age of son be ‘x’ years.
Then, father’s age = 4x years.
It is given that sum of their ages is 50 years.
So, x + 4x = 50
5x = 50
x = 10.
So, son’s age = 10 years.
Father’s age = 4x = 40 years.