# Solving Linear Equations

Worked-out examples on solving linear equations are given below. Instructions are given step-by-step with detailed explanation by using addition, subtraction, multiplication and division for solving linear equations.

### Examples on 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

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving 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 Linear Equations

Worksheet on Word Problems on Linear Equation

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