Updated By SaraNextGen

On March 11, 2024, 11:35 AM

Question 1:

Solve the linear equation 

Answer:

L.C.M. of the denominators, 2, 3, 4, and 5, is 60.

Multiplying both sides by 60, we obtain

⇒ 30x − 12 = 20x + 15 (Opening the brackets)

⇒ 30x − 20x = 15 + 12

⇒ 10x = 27

⇒ 

Question 2:

Solve the linear equation 

Answer:

L.C.M. of the denominators, 2, 4, and 6, is 12.

Multiplying both sides by 12, we obtain

6n − 9n + 10n = 252

⇒ 7n = 252

Question 3:

Solve the linear equation 

Answer:

L.C.M. of the denominators, 2, 3, and 6, is 6.

Multiplying both sides by 6, we obtain

6x + 42 − 16x = 17 − 15x

⇒ 6x − 16x + 15x = 17 − 42

⇒ 5x = −25

Question 4:

Solve the linear equation 

Answer:

L.C.M. of the denominators, 3 and 5, is 15.

Multiplying both sides by 15, we obtain

5(x − 5) = 3(x − 3)

⇒ 5x − 25 = 3x − 9 (Opening the brackets)

⇒ 5x − 3x = 25 − 9

⇒ 2x = 16

Question 5:

Solve the linear equation 

Answer:

L.C.M. of the denominators, 3 and 4, is 12.

Multiplying both sides by 12, we obtain

3(3t − 2) − 4(2t + 3) = 8 − 12t

⇒ 9t − 6 − 8t − 12 = 8 − 12t (Opening the brackets)

⇒ 9t − 8t + 12t = 8 + 6 + 12

⇒ 13t = 26

Question 6:

Solve the linear equation 

Answer:

L.C.M. of the denominators, 2 and 3, is 6.

Multiplying both sides by 6, we obtain

6m − 3(m − 1) = 6 − 2(m − 2)

⇒ 6m − 3m + 3 = 6 − 2m + 4 (Opening the brackets)

⇒ 6m − 3m + 2m = 6 + 4 − 3

⇒ 5m = 7

⇒ 

Question 7:

Simplify and solve the linear equation 

Answer:

3(t − 3) = 5(2t + 1)

⇒ 3t − 9 = 10t + 5 (Opening the brackets)

⇒ −9 − 5 = 10t − 3t

⇒ −14 = 7t

Question 8:

Simplify and solve the linear equation 

Answer:

15(y − 4) − 2(y − 9) + 5(y + 6) = 0

⇒ 15y − 60 − 2y + 18 + 5y + 30 = 0 (Opening the brackets)

⇒ 18y − 12 = 0

⇒ 18y = 12

⇒ 

Question 9:

Simplify and solve the linear equation 

Answer:

3(5z − 7) − 2(9z − 11) = 4(8z − 13)−17

⇒ 15z − 21 − 18z + 22 = 32z − 52 − 17 (Opening the brackets)

⇒ −3z + 1 = 32z − 69

⇒ −3z − 32z = −69 − 1

⇒ −35z = −70

⇒ 

Question 10:

Simplify and solve the linear equation 

Answer:

0.25(4f − 3) = 0.05(10f − 9)

Multiplying both sides by 20, we obtain

5(4f − 3) = 10f − 9

⇒ 20f − 15 = 10f − 9 (Opening the brackets)

⇒ 20f − 10f = − 9 + 15

⇒ 10f = 6

⇒