The DAV Class 6 Maths Solutions and **DAV Class 6 Maths Chapter 7 Brain Teasers **Solutions of Linear Equations offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 7 Brain Teasers Solutions

Question 1.

A. Tick (✓) the correct answer.

Twelve less than four times a number is 20, is represented by:

(i) 12 – 4x = 20

(ii) 20 = – 12 – 4x

(iii) 4x + 12 = 20

(iv) 4x – 12 = 20

Answer:

4x – 12 = 20

Hence, (iv) is the correct option.

(b) Which of the following equations has x = 3 as a solution?

(i) x – 2 = 5

(ii) x + 2 = 5

(iii) 2x + 1 = 0

(iv) x + 4 = 6

Answer:

On putting x = 3inx + 2 = 5,

we get 3 + 2 = 5, which is true.

Hence, (ii) is the correct option.

(c) The linear equation for 2 more than the sum of a and 4 is 8 will be:

(i) 2a + 4 = 8

(ii) 2(a + 4) = 8

(iii) (a + 4) + 2 = 8

(iv) a + 4 = 8

Answer:

(iii) (a + 4) + 2 = 8

Hence, (iii) is the correct option.

(d) Which of the following is an equation of the given sentence?

Anjali is 5 years older than Nanjani.

(i) 5 + A = N

(ii) A + N = 5

(iii) N – 5 = A

(iv) A = N + 5

Answer:

(iv) A = N + 5

Hence, (iv) is the correct option.

(e) Which of the following equations does not have a solution in integers?

(i) x + 1 = 1

(ii) x – 1 = 3

(iii) 2x + 1 = 6

(iv) 1 – x = 5

Answer:

2x + 1 = 6

2x = 6 – 1

⇒ 2x = 5

x = \(\frac{5}{2}\), which is not an integer.

Hence, (iii) is the correct option.

B. Answer the following questions.

(a) If x + 5 = 7, then 2x – 3 = ?

Answer:

x + 5 = 7 (given)

∴ x = 7 – 5 = 2

Then, 2x – 3 = 2(2) – 3 = 4- 3 = 1

(b) What is the solution of the equation 5x + 5 = – 40?

Answer:

5x + 5 = -40

5x = -40 – 5

5x = -45

x = \(\frac{-15}{5}\) = -9

(c) If 0.5y = 1.5, find y.

Answer:

0.5y = 1.5

y = \(\frac{1.5}{0.5}=\frac{15}{5}\) = 3

(d) Check if p = 4 is the solution of \(\frac{1}{2}\)(p + 3) = 7.

Answer:

On putting p = 4, we get

\(\frac{1}{2}\)(4 + 3) = \(\frac{1}{2}\) × 7 = \(\frac{7}{2}\)

\(\frac{7}{2}\) ≠ 7

(e) If \(\frac{x+2.4}{2}\) = 3, then find x.

Answer:

\(\frac{x+2.4}{2}\) = 3

x + 2.4 = 6

x = 6 – 2.4

or x = 3.6

Question 2.

Write any five linear equations:

Answer:

(i) x + 5 = 3

(ii) 2x + 3 = 7

(iii) 5x – 1 = 2x + 3

(iv) x + 1 = 2x – 3

(v) 2x + 5 = -4

Question 3.

Which side of the following equations is binomial?

(a) 2x + 1 = 7

(b) \(\frac{4}{5}\)y + 2 = 4

(c) 2(x + 3) = 8

Answer:

(a) LHS (2x + 1) is binomial

(b) LHS (\(\frac{4}{5}\)y + 2) is binomial

(c) LHS 2(x + 3) is binomial

Question 4.

Convert into linear equations:

(a) Thrice a number decreased by 5 is 9

(b) A number multiplied by two is 3 more than the number itself

(c) Twice a number subtracted from 13 is 5

(d) One-ninth of a number added to one is 11.

Answer:

(a) 3x – 5 = 9

(b) 2x = x + 3

(c) 13 – 2x = 5

(d) \(\frac{x}{9}\) + 1 = 11

Question 5.

Solve the following equations

(a) 4x – 3 = 2x + 1

Answer:

4x – 3 = 2x + 1

⇒ 4x -3 + 3 = 2x + l + 3 (Adding 3 to both sides)

⇒ 4x = 2x + 4

⇒ 4x – 2x = 4 (Shifting 2x to LHS)

⇒ 2x = 4

⇒ \(\frac{2 x}{2}=\frac{4}{2}\) (Dividing both sides by 2)

∴ x = 2

(b) 2(x – 5) = 10

Answer:

⇒ 2(x – 5) = 10

⇒ \(\frac{2(x-5)}{2}=\frac{10}{2}\) (Dividing both sides by 2)

⇒ x – 5 = 5

⇒ x – 5 + 5 = 5 + 5 (Adding 5 to both sides)

∴ x = 10

(c) \(\frac{x+8}{2}\) + 8 = 4

Answer:

⇒ \(\frac{x+8}{2}\) × 2 = 4 × 2 (Multiplying both sides by 2)

⇒ x + 8 = 8

⇒ x + 8 – 8 = 8 – 8 (Adding -8 to both sides)

∴ x = 0

(d) 0.5x = 25

Answer:

⇒ \(\frac{0.5 x}{0.5}=\frac{25}{0.5}\) (Dividing both sides by 0.5)

∴ x = 50

Question 5.

Solve the following equations and check the solutions:

(a) 1 – 4 x = -11

Answer:

1 – 4x = -11

⇒ -1 + 1- 4x = -11- 1 (Adding —1 to both sides)

⇒ -4x = -12

⇒ \(\frac{-4 x}{-4}=\frac{-12}{-4}\)(Dividing both sides by -4)

∴ x = 3

Check: 1 – 4x = -11

Putting x = 3

1 – 4 × 3 = -11

⇒ 1 – 12 = -11

∴ -11 = -11 (Hence Verified)

(b) y + \(\frac{3}{2}\) = 5

Answer:

∴ 5 = 5 (Hence Verified)

Question 6.

Complete the following statements with correct terms and signs:

(a) To solve the equation x + 3 = 8, we first add _____ to both sides.

Answer:

-3

(b) To solve the equation 9y = 72, we _____ LHS and RHS by 9.

Answer:

divide

(c) The solution of = 5 is _____

Answer:

z = 15

(d) To solve the equation 2x – 3 = 6, we first add ______ to both sides and then divide both sides by _____.

Answer:

3, 2

(e) The degree of variable in a linear equation is _____

Answer:

1

Additional Questions

Question 1.

Solve the following equations and check.

(a) \(\frac{x-1}{2}\) = 3 = 3

Answer:

\(\frac{x-1}{2}\) = 3 = 3

\(\frac{x-1}{2}\) x 2 = 3 x 2 (Multiplying both sides by 2)

⇒ x – 1 = 6

⇒ x – 1 + 1 = 6 + 1 (Adding 1 to both sides)

x = 7

Check: \(\frac{x-1}{2}\) = 3

Put x = 7

\(\frac{7-1}{2}\) = 3

⇒ \(\frac{6}{2}\) = 3

∴ 3 = 3 (Hence Verified)

(b) \(\frac{2 x+5}{3}\) = 7

\(\frac{2 x+5}{3}\) × 3 = 7 × 3

(Multiplying both sides by 3)

⇒ 2x + 5 = 21

⇒ 2x + 5 – 5 = 21- 5 (Adding -5 to both sides)

⇒ 2x = 16

⇒ \(\frac{2 x}{2}=\frac{16}{2}\) (Dividing both sides by 2)

x = 8

Check: \(\frac{2 \times 8+5}{3}\) = 7

Put x = 8

\(\frac{2 \times 8+5}{3}\) = 7

\(\frac{16+5}{3}\) = 7

\(\frac{21}{3}\) = 7

Question 2.

Find the numerical coefficients in the following terms:

(a) –\(\frac{2}{3}\)xy

(b) –\(\frac{1}{2}\)x<sup>2</sup>y

(c) -5pq

(d) -p

(e) 0

Answer:

(a) –\(\frac{2}{3}\)

(b) –\(\frac{1}{2}\)

(c) -5

(d) -1

(e) 0

Question 3.

Convert into linear equations:

(a) 5 is added to twice a number gives 17.

(b) Two-third of a number is added to itself gives 15.

(c) Twice a number subtracted from 13 is 5.

(d) One-eighth of a number is 2.

Answer:

(a) 2x + 5 = 17

(b) \(\frac{2}{3}\)x + x = 15

(c) 13 – 2x = 5

(d) \(\frac{1}{8}\)x = 2

Question 4.

Convert the following equations in statements:

(a) 2x + 5 = 11

(b) x + 5 = 15

(c) \(\frac{x}{2}\) – 5 = 7

(d) \(\frac{x}{2}\) – \(\frac{x}{3}\) = 1

(e) \(\frac{2y}{3}\) = 4

(f) 7y = 21

Answer:

(a) 5 is added to twice a number is 11.

(b) A number more than 5 is 15.

(c) 5 less than half of a number is 7.

(d) Difference between half and one-third of a number is 1.

(e) Two-third of a number is 4.

(f) Seven times a number is 21.

Question 5.

Fill in the blanks:

(a) To solve 3x + 5 = 10, we first add to both sides and then divide by _____

Answer:

– 5, 3

(b) The solution of = 6 is _____

Answer:

9

(c) 3 is the number satisfying the equation 2x + 7 = _____.

Answer:

13

(d) The number which satisfy the equation 3x + \(\frac{1}{2}=\frac{7}{2}\) is _____

Answer:

1

(e) The degree of the variable in a linear equation is __________.

Answer:

1