Rs Aggarwal 2019 Solutions for Class 7 Math Chapter 7 Linear Equations In One Variable are provided here with simple step-by-step explanations. These solutions for Linear Equations In One Variable are extremely popular among Class 7 students for Math Linear Equations In One Variable Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2019 Book of Class 7 Math Chapter 7 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2019 Solutions. All Rs Aggarwal 2019 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

3x − 5 = 0

#### Question 2:

8x − 3 = 9 − 2x

8x − 3 = 9 − 2x
$⇒$8x + 2x = 9 + 3                   (By transposition)
$⇒$10x = 12

7 − 5x = 5 − 7x

3 + 2x = 1 − x

#### Question 5:

2(x − 2) +3(4x − 1) = 0

#### Question 6:

5(2x − 3) − 3(3x − 7) = 5

#### Question 7:

$2x-\frac{1}{3}=\frac{1}{5}-x$

#### Question 8:

$\frac{1}{2}x-3=5+\frac{1}{3}x$

#### Question 9:

$\frac{x}{2}+\frac{x}{4}=\frac{1}{8}$

#### Question 10:

3x + 2(x + 2) = 20 − (2x − 5)

#### Question 11:

13(y − 4) − 3(y − 9) − 5(y + 4) = 0

#### Question 12:

$\frac{2m+5}{3}=3m-10$

#### Question 13:

6(3 x + 2) − 5(6x − 1) = 3(x − 8) − 5(7x − 6) + 9x

#### Question 14:

t − (2t + 5) − 5(1 − 2t) = 2(3 + 4t) −3(t − 4)

#### Question 15:

$\frac{2}{3}x=\frac{3}{8}x+\frac{7}{12}$

#### Question 16:

$\frac{3x-1}{5}-\frac{x}{7}=3$

#### Question 17:

$2x-3=\frac{3}{10}\left(5x-12\right)$

#### Question 18:

$\frac{y-1}{3}-\frac{y-2}{4}=1$

#### Question 19:

$\frac{x-2}{4}+\frac{1}{3}=x-\frac{2x-1}{3}$

#### Question 20:

$\frac{2x-1}{3}-\frac{6x-2}{5}=\frac{1}{3}$

#### Question 21:

$\frac{y+7}{3}=1+\frac{3y-2}{5}$

#### Question 22:

$\frac{2}{7}\left(x-9\right)+\frac{x}{3}=3$

#### Question 23:

$\frac{2x-3}{5}+\frac{x+3}{4}=\frac{4x+1}{7}$

#### Question 24:

$\frac{3}{4}\left(7x-1\right)-\left(2x-\frac{1-x}{2}\right)=x+\frac{3}{2}$

#### Question 25:

$\frac{x+2}{6}-\left(\frac{11-x}{3}-\frac{1}{4}\right)=\frac{3x-4}{12}$

#### Question 26:

$\frac{9x+7}{2}-\left(x-\frac{x-2}{7}\right)=36$

#### Question 27:

$0.5x+\frac{x}{3}=0.25x+7$

#### Question 28:

0.18(5x − 4) = 0.5x + 0.8

#### Question 29:

2.4(3 − x) − 0.6(2x − 3) = 0

#### Question 30:

0.5x −(0.8 − 0.2x) = 0.2 − 0.3x

#### Question 31:

$\frac{x+2}{x-2}=\frac{7}{3}$

#### Question 32:

$\frac{2x+5}{3x+4}=3$

#### Question 1:

Twice a number when decreased by 7 gives 45. Find the number.

#### Question 2:

Thrice a number when increased by 5 gives 44. Find the number.

#### Question 3:

Four added to twice a number yields $\frac{26}{5}$. Find the fractions.

#### Question 4:

A number when added to its half gives 72. Find the number.

#### Question 5:

A number added to its two-thirds is equal to 55. Find the number.

#### Question 6:

A number when multiplied by 4, exceeds itself by 45. Find the number.

#### Question 7:

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

#### Question 8:

$\frac{2}{3}$ of a number is less than the original number by 20. Find the number.

#### Question 9:

A number is $\frac{2}{5}$ times another number. If their sum is 70, find the numbers.

#### Question 10:

Two-thirds of a number is greater than one-third of the number by 3. Find the number.

#### Question 11:

The fifth part of a number when increased by 5 equals its fourth part decreased by 5. Find the number.

#### Question 12:

Find two consecutive natural numbers whose sum is 63.

#### Question 13:

Find two consecutive positive odd integers whose sum is 76.

#### Question 14:

Find two consecutive positive even integers whose sum is 90.

#### Question 15:

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.

#### Question 16:

A sum of 500 is in the form of denominations of 5 and 10. If the total number of notes is 90, find the number of notes of each type.

#### Question 17:

Sumitra has 34 in 50-paise and 25-paise coins. If the number of 25-paise coins is twice the number of 50-paise coins, how many coins of each kind does she have?

#### Question 18:

Raju is 19 years younger than his cousin. After 5 years, their ages will be in the ratio 2 : 3. Find their present ages.

#### Question 19:

A father is 30 years older than his son. In 12 years, the man will be three times as old as his son. Find their present ages.

#### Question 20:

The ages of Sonal and Manoj are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

#### Question 21:

Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

#### Question 22:

After 12 years Manoj will be 3 times as old as he was 4 years ago. Find his present age.

#### Question 23:

In an examination, a student requires 40% of the total marks to pass. If Rupa gets 185 marks and fails by 15 marks, find the total marks.

#### Question 24:

A number consists of two digits whose sum is 8. If 18 is added to the number its digits are reversed. Find the number.

#### Question 25:

The total cost of 3 tables and 2 chairs is 1850. If a table costs 75 more than a chair, find the price of each.

#### Question 26:

A man sold an article for 495 and gained 10% on it. Find the cost price of the article.

#### Question 27:

The length of a rectangular field is twice its breadth. If the perimeter of the field is 150 metres, find its length and breadth.

#### Question 28:

Two equal sides of a triangle are each 5 metres less than twice the third side. If the perimeter of the triangle is 55 metres, find the lengths of its sides.

#### Question 29:

Two complementary angles differ by 80. Find the angles.

#### Question 30:

Two supplementary angles differ by 440. Find the angles.

#### Question 31:

In an isosceles triangle the base angles are equal and the vertex angle is twice of each base angle. Find the measures of the angles of the triangle.

#### Question 32:

A man travelled $\frac{3}{5}$ of his journey by rail, $\frac{1}{4}$ by a taxi, $\frac{1}{8}$ by a bus and the remaining 2 km on foot. What is the length of his total journey?

#### Question 33:

A labourer is engaged for 20 days on the condition that he will receive 120 for each day he works and will be fined 10 for each day he is absent. If he receives 1880 in all, for how many days did he remain absent?

#### Question 34:

Hari Babu left one-third of his property to his son, one-fourth to his daughter and the remainder to his wife. If his wife's share is 18000, what was the worth of his total property?

#### Question 35:

How much pure alcohol must be added to 400 mL of a 15% solution to make its strength 32%.

#### Question 1:

Mark (âœ“) against the correct answer

If $5x-\frac{3}{4}=2x-\frac{2}{3},$ then x = ?

(a) $\frac{1}{12}$
(b) $\frac{1}{4}$
(c) 36
(d) $\frac{1}{36}$

#### Question 2:

Mark (âœ“) against the correct answer

If $2z+\frac{8}{3}=\frac{1}{4}z+5,$ then z = ?

(a) 3
(b) 4
(c) $\frac{3}{4}$
(d) $\frac{4}{3}$

#### Question 3:

Mark (âœ“) against the correct answer

If (2n + 5) = 3(3n − 10), then n = ?

(a) 5
(b) 3
(c) $\frac{2}{5}$
(d) $\frac{2}{3}$

#### Question 4:

Mark (âœ“) against the correct answer

If $\frac{x-1}{x+1}=\frac{7}{9},$ then x = ?

(a) 6
(b) 7
(c) 8
(d) 10

#### Question 5:

Mark (âœ“) against the correct answer

If 8(2x − 5) − 6(3x − 7) = 1, then x = ?

(a) 2
(b) 3
(c) $\frac{1}{2}$
(d) $\frac{1}{3}$

#### Question 6:

Mark (âœ“) against the correct answer

If $\frac{x}{2}-1=\frac{x}{3}+4,$ then x = ?

(a) 8
(b) 16
(c) 24
(d) 30

#### Question 7:

Mark (âœ“) against the correct answer

If $\frac{2x-1}{3}=\frac{x-2}{3}+1,$ then x = ?

(a) 2
(b) 4
(c) 6
(d) 8

#### Question 8:

The sum of two consecutive whole numbers is 53. The smaller number is

(a) 25
(b) 26
(c) 29
(d) 23

#### Question 9:

The sum of two consecutive even numbers is 86. The larger of the two is

(a) 46
(b) 36
(c) 38
(d) 44

#### Question 10:

The sum of two consecutive odd numbers is 36. The smaller one is

(a) 15
(b) 17
(c) 19
(d) 13

#### Question 11:

on adding 9 to the twice of a whole number gives 31. The whole number is

(a) 21
(b) 16
(c) 17
(d) 11

#### Question 12:

Thrice a number when increased by 6 gives 24. The number is

(a) 6
(b) 7
(c) 8
(d) 11

#### Question 13:

$\frac{2}{3}$ of a number is less than the original number by 10. The original number is

(a) 30
(b) 36
(c) 45
(d) 60

#### Question 14:

Two complementary angles differ by 10°. The larger angle is

(a) 60°
(b) 50°
(c) 64°
(d) 54°

#### Question 15:

Two supplementary angles differ by 20°. The smaller of the two measures

(a) 60°
(b) 80°
(c) 100°
(d) 120°

#### Question 16:

The ages of A and B are in the ratio 5 : 3. After 6 years, their ages will be in the ratio 7 : 5. The present age of A is

(a) 5 years
(b) 10 years
(c) 15 years
(d) 20 years

#### Question 17:

A number when multiplied by 5 is increased by 80. The number is

(a) 15
(b) 20
(c) 25
(d) 30

#### Question 18:

The length of a rectangle is three times its width and its perimeter is 96 m. The length is

(a) 12 m
(b) 24 m
(c) 36 m
(d) 48 m

#### Question 1:

Evaluate x3 + y3 + z3 −3xyz when x = −2, y = −1 and z = 3.

#### Question 2:

Write the coefficient of x in each of the following:

(i) −5xy
(ii) 2xy2z
(iii) $-\frac{3}{2}abc$

#### Question 3:

Subtract x2− 2xy + 5y2 − 4 from 4xy − 5x2y2 + 6.

#### Question 4:

How much less is x2− 2xy + 3y2than 2x2 − 3y2 + xy?

#### Question 5:

Find the product $\left(\frac{3}{5}ab{c}^{3}\right)×\left(\frac{-25}{12}{a}^{3}{b}^{2}\right)×\left(-8{b}^{3}c\right).$

#### Question 6:

Simplify:

(3a + 4)(2a − 3) + (5a − 4)(a + 2)

#### Question 7:

Solve: $\frac{3x}{10}+\frac{2x}{5}=\frac{7x}{25}+\frac{29}{25}.$

#### Question 8:

Solve: $0.5x+\frac{x}{3}=0.25x+7.$

#### Question 9:

The sum of two consecutive odd numbers is 68. Find the numbers.

#### Question 10:

Reenu's father is thrice as old as Reenu. After 12 years he will be just twice his daughter. Find their present ages.

#### Question 11:

Mark (âœ“) against the correct answer
If $2x+\frac{5}{3}=\frac{1}{4}x+4,$ then x = ?
(a) 3
(b) 4
(c) $\frac{3}{4}$
(d) $\frac{4}{3}$

#### Question 12:

Mark (âœ“) against the correct answer
If $\frac{x}{2}-\frac{x}{3}=5$ then x = ?
(a) 8
(b) 16
(c) 24
(d) 30

#### Question 13:

Mark (âœ“) against the correct answer
If $\frac{x-2}{3}=\frac{2x-1}{3}-1,$ then x = ?
(a) 2
(b) 4
(c) 6
(d) 8

#### Question 14:

Mark (âœ“) against the correct answer
A number when multiplied by 4 is increased by 54. The number is

(a) 21
(b) 16
(c) 18
(d) 19

#### Question 15:

Two complementary angles differ by 14°. The larger angle is

(a) 50°
(b) 52°
(c) 54°
(d) 56°

#### Question 16:

The length of a rectangle is twice its breadth and its perimeter is 96 m. The length of the rectangle is

(a) 28 m
(b) 30 m
(c) 32 m
(d) 36 m

#### Question 17:

The ages of A and B are in the ratio 4 : 3. After 6 years, their ages will be in the ratio 11 : 9. A's present age is

(a) 12 years
(b) 16 years
(c) 20 years
(d) 24 years

#### Question 18:

Fill in the blanks

(i) −2a2b is a ...... .
(ii) (a2 − 2b2) is a ...... .
(iii) (a + 2b − 3c) is a ...... .
(iv) In −5ab, the coefficient of a is ...... .
(v) In x2 + 2x − 5, the ...... term is −5.

(i) −2a2b is a monomial.
(ii) (a2 − 2b2) is a binomial.
(iii) (a + 2b − 3c) is a trinomial.
(iv) In −5ab, the coefficient of a is -5b.
(v) In x2 + 2x − 5, the constant term is −5.

#### Question 19:

Write 'T' for true and 'F' for false

(i) In −x, the constant term is −1.
(ii) The coeffiecient of x in x2 − 3x + 5 is 3.
(iii) (5x − 7) − (3x − 5) = 2x − 12.
(iv) (3x + 5y)(3x − 5y) = (9x2 − 25y2).
(v) If a = 2 and b = $\frac{1}{2},$ then the value of ab (a2 + b2) is $4\frac{1}{4}$.