Linear equations examples and answers Class 8

 

Linear equations

An equation of degree 1 containing only one variable is called a simple linear equation.

Rule for solving linear equatons

1 : Same number or expression can be added to both sides of an equation.

2.  

Same number or expression can be subtracted from both sides of an equation.

3. Both sides of an equation can be multiplied by the same non-zero number or expression.

4. Both sides of an equation can be divided by the same non-zero number or expression.

Linear equations examples and answers  :

Exercise 15A

1. 4x - 9 = 2x + 7

 ⇒ 4x - 2x = 7 + 9

 ⇒ 2x = 16

 ⇒ x = 16/2

 ⇒ x = 8

2. 5y + 18 = 11 - 2y 

⇒ 5y + 2y = 11 - 18

⇒ 7y = -7

⇒ y = -7/7

⇒ y = -1

3. 21 - 3( x - 7 ) = x + 20

⇒ 21 -3x + 21 = x + 20

⇒ 42 - 3x = x + 20

⇒ 42 -20 = x + 3x

⇒ 22 = 4x 

⇒ x = 22 / 4

⇒ x = 11 / 2

4. 3( y - 7 ) - 2( 3y - 4 ) = ( 2 - 5y )

⇒ 3y - 21 - 6y + 8 = 2 - 5y    --------------- ( solving bracket )

⇒ 3y - 6y + 5y = 2 - 8 + 21

⇒ 2y = 15

⇒ y = 15/2

5. 3( t - 5) - 16t = 12 - 2(t - 3 )

⇒ 3t -15 - 16t = 12 - 2t + 6

⇒ 3t -16t + 2t = 12 + 6 +15

⇒ - 11t = 33

⇒ t = 33/ -11

⇒ t = -3 

6. 3x/4 - ( x - 4)/3 = 5/3

⇒ 3x * 3/ 4*3 - 4(x - 4) / 3*4 = 5/3

⇒ 9x /12 - 4x + 16 /12 = 5/3

⇒ 9x - 4x + 16 /12 = 5/3

⇒ 5x + 16 /12 = 5/3

⇒ 5x + 16 = (5/3) * 12

⇒ 5x + 16 = 5 * 4

⇒ 5x = 20 - 16

⇒ 5x = 4 

⇒ x = 4 / 5

7. ( 4x + 1)/ 3 + (2x - 1)/2 - (3x - 7)/5 = 6

8. ( z + 5) / 6 - (z + 1 )/ 9 =( z + 3) / 4

9. 2 - 9z / 17 - 4z = 4 / 5

10 . 2x - 3/ 3x - 1 = 2x + 3 / 3x + 4

 Word Problem based on Linear equations 

Method :

step 1. Read the problem carefully and determine the quantity to be found.

step 2 : Assign a letter (say x) to the unknown quantity.

step 3 : Using the given data, formulate the linear equation in the variable x.

step 4 : Solve the resulting equation.

Exercise : 

1) 17 less than 4 times a number is 11. Find the number.

Ans : Let the number be x.

          According to the question,

            4x - 17 = 11

         ⇒ 4x = 11 + 17

          ⇒ 4x = 28

          ⇒ x = 28 / 4

          ⇒ x = 7

          so, the number is 7

2) If 10 be added to four times a certain number, the result is 5 less than five times the number.

Ans : Let the number be x.

          According to the question,   

         4x + 10 = 5x -5

       ⇒ 4x - 5x = -5 -10

      ⇒ -x = -15

      ⇒ x = 15

       so, the number is 15

3) 2/3 of a number is 20 less than the original number. Find the original number.

Ans : Let the original number be x.

          According to the question,     

           x -20 = (2/3)x

        ⇒ x - (2/3) x = 20  --------- ( making denominator same for subtraction)

        ⇒  3x - 2x /3 = 20

        ⇒ x = 20 * 3

        ⇒ x = 60

         so, the number is 60

4)  A number is 25 more than its 5/6 th part. Find the number.

Ans :  Let the number be x.

          According to the question,

             x = 5x/6 +25

         ⇒ x - 5x/6 = 25

         ⇒ 6x - 5x /6 = 25

         ⇒ x = 25 * 6

         ⇒ x = 150

          so, the number is 150.

5) A number is as much greater than 21 as is less than 71. Find the number.

 Ans :  Let the number be x.

          According to the question,

            x - 21 = 71 - x

          ⇒ x + x = 71 + 21

         ⇒ 2x = 92

        ⇒ x = 92 / 2

        ⇒ x = 46 

         so, the number is 46.

6) 6 more than one forth of a number is two-fifths of the number. Find the number.

Ans :  Let the number be x.

          According to the question,

         x/4 + 6 = 2x/5

     ⇒  x/4 - 2x/5 = -6

     ⇒ 5x - 8x / 20 = -6 

      ⇒ -3x = -6 * 20

      ⇒  -3x = -120 

    ⇒ x = -120 / -3

      ⇒ x = 40

      so, the number is 40.

7) One -third of a number exceeds one fourth of the number by 15 . Find the number.

Ans :  Let the number be x.

          According to the question,

       x/3 = x/4 + 15

      ⇒ x/3 - x/4 = 15

      ⇒  4x - 3x / 12 = 15 

      ⇒ x = 15 * 12

      ⇒ x = 180

         so, the number is 180.

8) If one- fifth of a number decreased by 5 is 16, find the number.

Ans :   Let the number be x.

          According to the question,

       x/5 -5 = 16

       ⇒ x /5 = 16 + 5

      ⇒  x/5 = 21

      ⇒ x = 21 * 5

     ⇒ x = 105

         so, the number is 105.

9) Two number are in the ratio 3:4 and their sum is 84. Find the number.

Ans :   Let the number be x.

          According to the question,

         3x + 4x = 84

       ⇒ 7x = 84

       ⇒ x = 84 / 7

       ⇒ x = 12

      so, the number is 12.

10) Two number are in the ratio 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5 : 7. Find the original numbers.

Ans :