Linear Equations in One Variable

Exercise: 2.1

Solve the following equations and check your results.

1). 3x = 2x + 18

     3x – 2x = 18                  transposing 2x to LHS

       x = 18

 

2). 5t – 3 = 3t – 5

     5t – 3t = – 5 + 3

     2t = – 2

       t = ^–2/₂

       t = – 1             

3). 5x + 9 = 5 + 3x

     5x – 3x = 5 – 9

     2x = – 4

       x = ^–4/₂

       x = – 2

4). 4z + 3 = 6 + 2z

     4z – 2z = 6 – 3

      2z = 3

       z = ³/₂

5). 2x – 1 = 14 – x

     2x + x = 14 + 1

       3x = 15

       x = ¹⁵/₃

       x = 5    

 6). 8x + 4 = 3 (x – 1) + 7

     8x + 4 = 3x – 3 + 7

     8x + 4 = 3x + 4

     8x – 3x = 4 – 4

       5x = 0

       x = ⁰/₅

       x = 0  

7). x = ⁴/₅  (x + 10)

     5x =4(x + 10)

     5x = 4x + 40

     5x – 4x = 40

       x = 40  

8). ^2x/₃ + 1 = ^7x/₁₅ + 3

    ^2x/₃ – ^7x/₁₅ = 3 – 1                         LCM of 3 and 5 is 15

    ^10x/₁₅ – ^7x/₁₅ = 2

     ^10x-7x/₁₅ = 2

       ^3x/₁₅ = 2

       ^x/₅ = 2

       x = 2 X 5

       x = 10      

9). 2y + ⁵/₃ = ²⁶/₃ – y

    2y + y = ²⁶/₃ – ⁵/₃

    3y = ⁽²⁶ – ⁵⁾/₃

    3y = ²¹/₃

    3y = 7

     y = ⁷/₃

10). 3m = 5m – ⁸/₅

       3m – 5m = ^{– 8}/₅

       2m = ^-8/₅

       m = ^-8/₅ X ½

       m = ⁴/₅

Click here for the solutions of Std 8 Maths

1). Rational Numbers

 Exercise 1.1

2). Linear Equations in One Variable

Exercise 2.1

Exercise 2.2

3). Understanding Quadrilaterals

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

4). Data Handling

Exercise 4.1

Exercise 4.2