Do you want to learn how to solve linear equations? Then stay on this page, here we are giving the detailed steps of solving the linear equations. Go through the simple steps and some worked example problems to get a clear idea on the topic. You can easily solve the linear equations by using addition, subtraction, multiplication, and division operations.
Steps to Solve a Linear Equation
Have a look at the detailed steps and solve the linear equations effortlessly. Follow the guidelines and arrive at the solutions easily. They are as follows
- Transfer variables to one side and constants to the other side of the equation.
- Use arithmetic operations to transfer those.
- Find the value of a variable.
- The variable value becomes the required solution.
Linear Equations Questions with Solutions
Example 1.
Solve the equation (x + 4) / 2 = 8 + (x – 6) / 5 and verify your answer?
Solution:
Given linear equation is (x + 4) / 2 = 8 + (x – 6) / 5
(x + 4) / 2 = [40 + (x – 6)] / 5
Cross multiply the fraction.
5(x + 4) = 2(40 + x – 6])
5x + 20 = 2(x + 34)
5x + 20 = 2x + 68
Transferring 2x to L.H.S. changes to negative 2x and 20 to R.H.S. changes to -20.
5x – 2x = 68 – 20
3x = 48
x = 48/3
x = 16
Therefere, x = 16 is the solution for the equation.
Verification:
L.H.S = (x + 4) / 2
Put x = 16
L.H.S = (16 + 4) / 2
= 20/2 = 20
R.H.S = 8 + (x – 6) / 5
Put x = 16
R.H.S = 8 + (16 – 6) / 5
= 8 + 10/5
= (40 + 10) / 5
= 50/5 = 10
Since, L.H.S = R.H.S, verified.
Example 2.
Solve the equation 12 – x/6 = 7?
Solution:
Given linear equation is 12 – x/6 = 7
(72 – x) / 6 = 7/1
Cross multiply.
72 – x = 7 x 6
72 – x = 42
72 – 42 = x
30 = x
x = 30
Therefore, x = 30 is the solution for the equation.
Example 3.
Solve the equation 3(x – 3) = 4(2x + 1) and represent the solution graphically?
Solution:
Given linear equation is 3(x – 3) = 4(2x + 1)
3x – 9 = 8x + 4
-9 – 4 = 8x – 3x
-15 = 5x
x = -15/5
x = -3
Therefore, x = -3 is the solution for the equation.
Example 4.
Solve (x + 5) / (x – 5) = 1/2?
Solution:
Given linear equation is (x + 5) / (x – 5) = 1/2
Cross multiply the fraction
2(x + 5) = x – 5
2x + 10 = x – 5
2x – x = -5 – 10
x = -15
Therefore, x = -15 is the solution for the equation.