R d sharma solutions mathematics class 7 Solutions for Chapter 8 linear equations in one variable

Verify by substitution that:

(i) x = 4 is the root of 3x – 5 = 7

(ii) x = 3 is the root of 5 + 3x = 14

(iii) x = 2 is the root of 3x – 2 = 8x – 12

(iv) x = 4 is the root of (3x/2) = 6

(v) y = 2 is the root of y – 3 = 2y – 5

(vi) x = 8 is the root of (1/2)x + 7 = 11

Solve each of the following equations by trial – and – error method:

(i) x + 3 =12

(ii) x -7 = 10

(iii) 4x = 28

(iv) (x/2) + 7 = 11

(v) 2x + 4 = 3x

(vi) (x/4) = 12

(vii) (15/x) = 3

(viii) (x/18) = 20

Solve each of the following equations and check your answers:

x – 3 = 5

Solve the following equations

x + 9 = 13

Solve the following equations

x – (3/5) = (7/5)

Solve the following equations

3x = 0

Solve the following equations

(x/2) = 0

Solve the following equations

x – (1/3) = (2/3)

Solve the following equations

x + (1/2) = (7/2)

Solve the following equations

10 – y = 6

Solve the following equations

7 + 4y = -5

Solve the following equations

(4/5) – x = (3/5)

Solve the following equations

2y – (1/2) = (-1/3)

Solve the following equations

14 = (7x/10) – 8

Solve the following equations

3 (x + 2) = 15

Solve the following equations

(x/4) = (7/8)

Solve the following equations

(1/3) – 2x = 0

Solve the following equations

3 (x + 6) = 24

Solve the following equations

3 (x + 2) – 2 (x – 1) = 7

Solve the following equations

8 (2x – 5) – 6(3x – 7) = 1

Solve the following equations

6 (1 – 4x) + 7 (2 + 5x) = 53

Solve the following equations

5 (2 – 3x) -17 (2x -5) = 16

Solve the following equations

(x – 3)/5 -2 = -1

Solve the following equations

5 (x – 2) + 3 (x +1) = 25

Solve the following equations. Also, verify the result.

6x + 5 = 2x + 17

Solve the following equations. Also, verify the result.

2 (5x – 3) – 3 (2x – 1) = 9

Solve the following equations. Also, verify the result.

(x/2) = (x/3) + 1

Solve the following equations. Also, verify the result.

(x/2) + (3/2) = (2x/5) – 1

Solve the following equations. Also, verify the result.

(3/4) (x -1) = (x – 3)

Solve the following equations. Also, verify the result.

3 (x – 3) = 5 (2x + 1)

Solve the following equations. Also, verify the result.

3x – 2 (2x -5) = 2 (x + 3) – 8

Solve the following equations. Also, verify the result.

x – (x/4) – (1/2) = 3 + (x/4)

Solve the following equations. Also, verify the result.

(6x – 2)/9 + (3x + 5)/18 = (1/3)

Solve the following equations. Also, verify the result.

m – (m – 1)/2 = 1 – (m – 2)/3

Solve the following equations. Also, verify the result.

(5x – 1)/3 – (2x – 2)/3 = 1

Solve the following equations. Also, verify the result.

0.6x + 4/5 = 0.28x + 1.16

Solve the following equations. Also, verify the result.

0.5x + (x/3) = 0.25x + 7

If 5 is subtracted from three times a number, the result is 16. Find the number.

Find the number which when multiplied by 7 is increased by 78.

Find three consecutive natural numbers such that the sum of the first and second is 15 more than the third.

The difference between two numbers is 7. Six times the smaller plus the larger is 77. Find the numbers.

A man says, “I am thinking of a number. When I divide it by 3 and then add 5, my answer is twice the number I thought of”. Find the number.

If a number is tripled and the result is increased by 5, we get 50. Find the number.

Shikha is 3 years younger to her brother Ravish. If the sum of their ages 37 years, what are their present age?

Mrs Jain is 27 years older than her daughter Nilu. After 8 years she will be twice as old as Nilu. Find their present ages?

A man 4 times as old as his son. After 16 years, he will be only twice as old as his son. Find their present ages.

The difference in age between a girl and her younger sister is 4 years. The younger sister in turn is 4 years older than her brother. The sum of the ages of the younger sister and her brother is 16. How old are the three children?

One day, during their vacation at beach resort, Shella found twice as many sea shells as Anita and Anita found 5 shells more than sandy. Together sandy and Shella found 16 sea shells. How many did each of them find?

Andy has twice as many marbles as Pandy, and Sandy has half as many has Andy and Pandy put together. If Andy has 75 marbles more than Sandy. How many does each of them have?

A bag contains 25 paise and 50 paise coins whose total value is Rs 30. If the number of 25 paise coins is four times that of 50 paise coins, find the number of each type of coins.

The length of a rectangular field is twice its breadth. If the perimeter of the field is 228 meters, find the dimensions of the field.

There are only 25 paise coins in a purse. The value of money in the purse is Rs 17.50. Find the number of coins in the purse.

In a hostel mess, 50kg rice are consumed every day. If each student gets 400gm of rice per day, find the number of students who take meals in the hostel mess.