Workedout examples on solving linear equations are given below. Instructions are given stepbystep with detailed explanation by using addition, subtraction, multiplication and division for solving linear equations.
1. Solve: (2x + 5)/(x + 4) = 1
Solution:
(2x + 5)/(x + 4) = 1
⇒ 2x + 5 = 1(x + 4)
⇒ 2x + 5 = x + 4
⇒ 2x  x = 4  5 (Transferring positive x to the left hand side changes to negative x and again, positive 5 changes to negative 5)
⇒ x = 1
Therefore, x =  1 is the required solution of the equation (2x + 5)/(x + 4) = 1
2. Solve: 6x  19 = 3x  10
Solution:
6x  19 = 3x  10
⇒ 6x  3x =  10 + 19 (Transferring 3x to L.H.S changes to negative 3x and 19 to R.H.S. changes to positive 19)
⇒ 3x = 9
⇒ 3x/3 = 9/3 (Dividing both sides by 3)
⇒ x = 3
3. Solve: 5  2(x  1) = 4(3  x)  2x.
Solution:
5  2(x  1) = 4(3  x)  2x
⇒ 5  2x + 2 = 12  4x  2x (Removing the brackets and then simplify)
⇒ 7  2x = 12  6x (Transferring 6x to L.H.S. changes to positive 6x and 7 to R.H.S. changes to negative 7)
⇒ 2x + 6x = 12  7
⇒ 4x = 5
⇒ 4x/4 = 5/4
⇒ x = 5/4
4. x/2 + x/3 = x  7
Solution:
x/2 + x/3 = x  7
Least common multiple of2 and 3 is 6
⇒ (x/2 × 3/3) + (x/3 × 2/2) = x  7
⇒ 3x/6 + 2x/6 = x  7
⇒ (3x + 2x)/6 = x  7
⇒ 5x/6 = x  7
⇒ 5x = 6(x  7)
⇒ 5x = 6x  42 (Transferring 6x to L.H.S. changes to negative 6x)
⇒ 5x  6x = 42
⇒ x = 42
⇒ x = 42
5. 2/(x + 3) = 3/(5  x)
Solution:
2/(x + 3) = 3/(5  x)
⇒ 3(x + 3) = 2(5  x) (cross multiply and then remove the brackets)
⇒ 3x + 9 = 10  2x (Transferring 2x to L.H.S. changes to positive 2x and 9 to R.H.S. changes to 9)
⇒ 3x + 2x = 10  9
⇒ 5x = 1
⇒ 5x/5 = 1/5 (Dividing both sides by 5)
⇒ x = 1/5
● Equations
How to Solve Linear Equations?
Problems on Linear Equations in One Variable
Word Problems on Linear Equations in One Variable
Practice Test on Linear Equations
Practice Test on Word Problems on Linear Equations
● Equations  Worksheets
Worksheet on Word Problems on Linear Equation
7th Grade Math Problems
8th Grade Math Practice
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