2 Marks Questions

Question 12 Marks

Solve these equation:
10 – 5x = 3(x – 4) – 2(x – 7)

Answer

10 – 5x = 3(x – 4) – 2(x – 7)
⇒ 10 – 5x = 3x – 12 – 2x + 14
⇒ 10 – 5x = 3x – 2x – 12 + 14
⇒ 10 – 5x = x + 2
⇒ 10 – 2 = x + 5x
⇒ 8 = 6x
$\Rightarrow x=\frac{4}{3}$

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Question 22 Marks

Solve these equation:
2x + 1 = 6 – (2x – 3)

Answer

2x + 1 = 6 – (2x – 3)
⇒ 2x + 1 = 6 – 2x + 3
⇒ 2x + 2x = 6 + 3 – 1
⇒ 4x = 8
⇒ x = 2

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Question 32 Marks

Solve these equation:
3 – 7s = 7 – 3s

Answer

3 – 7s = 7 – 3s
⇒ 3 – 7 = -3s + 7s
⇒ -4 = 4s
⇒ s = -1

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Question 42 Marks

Solve these equation:
6(x – 1) = 2(x – 1) – 4

Answer

6(x – 1) = 2(x – 1) – 4 [Distributive property]
⇒ 6x – 6 = 2x – 2 – 4
⇒ 6x – 6 = 2x – 6
⇒ 6x – 2x = -6 + 6
⇒ 4x = 0
⇒ x = 0

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Question 52 Marks

Solve these equation:
2(x – 4) = -16

Answer

2(x – 4) = -16
⇒ x – 4 = -8
⇒ x = -8 + 4
⇒ x = -4

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Question 62 Marks

Solve these equation:
2(7 – 2n) = -6

Answer

2(7 – 2n) = -6
⇒ 2 × (7 – 2n) = -6
⇒ 7 – 2n = -6 ÷ 2
⇒ 7 – 2n = -3
⇒ -2n = -3 – 7
⇒ -2n = -10
⇒ n = 5

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Question 72 Marks

Solve these equation:
-3(u + 2) = 2(u – 1)

Answer

-3(u + 2) = 2(u – 1)
⇒ -3u – 6 = 2u – 2
⇒ -3u – 2u = -2 + 6
⇒ -5u = 4
$\Rightarrow u=\frac{-4}{5}$

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Question 82 Marks

Solve these equation:
5(r + 2) = 10

Answer

5(r + 2) =10
⇒ 5 × (r + 2) = 10
⇒ (r + 2) = 10 ÷ 5
⇒ r + 2 = 2
⇒ r = 2 – 2
⇒ r = 0

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Question 92 Marks

A number increased by 36 is equal to ten times itself. What is the number?

Answer

Let the number be x.
According to the question
x + 36 = 10 × x
⇒ x + 36 = 10x
⇒ 36 = 10x – x
⇒ 36 = 9x
⇒ 36 ÷ 9 = x
⇒ 4 = x

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Question 102 Marks

The steps to solve equation are shown below. Identify and correct any mistakes:
14y + 24 = 36
7y + 12 = 18
7y = 6
$y=\frac{6}{7}$

Answer

14y + 24 = 36
7y + 12 = 18 [Dividing by 2 throughout]
7y = 6
$y=\frac{6}{7} \rightarrow$ No Error

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Question 112 Marks

The steps to solve equation are shown below. Identify and correct any mistakes:
6x + 9 = 66
x + 9 = 11
x = 11 – 9
x = 2

Answer

6x + 9 = 66 → Error
Variable terms should be on one side and constants on the other side before separating the coefficient from the variable.
Correction
6x + 9 = 66
6x = 66 – 9
6x = 57
$\begin{array}{l}X=\frac{57}{6} \\ X=\frac{19}{2}\end{array}$
$x=9 \frac{1}{2}$

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Question 122 Marks

The sum of two numbers is 76. One number is three times the other number. What are the numbers?

Answer

Let the two numbers be x and 3x.
According to the question
x + 3x = 76
⇒ 4x = 76
⇒ x = 19
The two numbers are 19 and 3 × 19, i.e., 19 and 57.

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Question 132 Marks

A taxi driver charges a fixed fee of ₹ 800 per day plus ₹ 20 for each kilometer traveled. If the total cost for a taxi ride is ₹ 2200, determine the number of kilometres traveled.

Answer

Fixed charges by Taxi driver = ₹ 800
Charge per kilometer = ₹ 20
Let the distance covered be x km.
According to the question
x × 20 + 800 = 2200
⇒ 20x = 2200 – 800
⇒ 20x = 1400
⇒ x = 70
Total distance covered is 70 km.

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Question 142 Marks

Here are machines that take an input, perform an operation on it, and send out the result as an output.

Find the inputs in the following cases:

Answer

(i) $\xrightarrow{(9)}+3 \xrightarrow{(12)} \times 4 \xrightarrow{(48)}-5=43$
(ii) $17+3 \xrightarrow{20} \times 4 \xrightarrow{80}-5=75$

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Question 152 Marks

Fill in the blank with integer:
-3 × (-11 + _______) = 45

Answer

Let unknown be y.
-3 × (-11 + y) = 45
⇒ (-11 + 7) = 45 ÷ (-3)
⇒ -11 + y = -15
⇒ y = -15 + 11
⇒ y = -4
∴ -3 × (-11 + (-4)) = 45

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Question 162 Marks

Fill in the blank with integer:
37 – (33 – _______) = 35

Answer

Let unknown be x.
37 – (33 – x) = 35
⇒ 37 – 33 + x = 35
⇒ 4 + x = 35
⇒ x = 35 – 4
⇒ x = 31
∴ 37 – (33 – 31) = 35

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Question 172 Marks

Fill in the blank with integer:
5 × _______ -8 = 37

Answer

Let unknown be x.
5 × x – 8 = 37
⇒ 5x – 8 = 37
⇒ 5x = 37 + 8
⇒ 5x = 45
⇒ x = 45 ÷ 5
⇒ x = 9
∴ 5 × 9 – 8 = 37

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Question 182 Marks

Find the value of each unknown:
3n = 10 + n

Answer

3n = 10 + n
Subtract n from both sides
3n – n = 10 + n – n
⇒ 2n = 10
Divide both sides by 2
$\begin{array}{l}\frac{2 n}{2}=\frac{10}{2} \\ \Rightarrow n=5\end{array}$

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Question 192 Marks

Find the value of each unknown:
7m = m – 3

Answer

7m = m – 3
Subtract m from both sides
7m – m = m – 3 – m
⇒ 6m = -3
Divide both sides by 6
$\begin{array}{l}\frac{6 m}{6}=-\frac{3}{6} \\ \Rightarrow m=-\frac{1}{2}\end{array}$

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Question 202 Marks

Find the value of each unknown:
k + 8 = 12 – k

Answer

k + 8 = 12 – k
Add k on both sides
k + 8 + k = 12 – k + k
⇒ 2k + 8 = 12
Subtract 8 from both sides
2k + 8 – 8 = 12 – 8
⇒ -2k = 4
Divide both sides by 2
$\frac{2 k}{2}=\frac{4}{2}$
⇒ k = 2

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Question 212 Marks

Find the value of each unknown:
13 – z = 8

Answer

13 – z = 8
Subtract 13 from both sides
13 – z – 13 = 8 – 13
⇒ -z = -5
Divide both sides by -1
$\frac{-z}{-1}=\frac{-5}{-1}$
⇒ z = +5

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Question 222 Marks

Find the value of each unknown:
-53w = -15

Answer

-53w = -15
Divide both sides by -53
$\frac{-53 w}{-53}=\frac{-15}{-53}$
$\Rightarrow W=\frac{15}{53}$

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Question 232 Marks

Find the value of each unknown:
-8 = 5x – 3

Answer

-8 = 5x – 3
Add 3 on both sides
-8 + 3 = 5x
⇒ -5 = 5x
Divide both sides by 5
$\frac{-5}{5}=\frac{5 x}{5}$
⇒ -1 = x

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Question 242 Marks

Find the value of each unknown:
2y = 60

Answer

2y = 60
Divide both sides by 2
$\frac{2 y}{2}=\frac{60}{2}$
⇒ y = 30

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Question 252 Marks

Frame an equation that has no solution.
[Hint: 4 more than a number, and 5 more than a number can never be equal!]

Answer

Equation u + 6 = u + 2 has no solution
Subtract u from both sides
u + 6 – u = u + 2 – u
⇒ 6 = 2, which is an incorrect statement.

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