NCERT Solutions Class 8 Mathematics Linear Equations in One Variable Ex 2.6

Class 8 - Mathematics
Linear Equations in One Variable - Exercise 2.6

Top Block 1

Solve the following equations.

Question: 1. Solve :

Answer :

⇒ 8𝓍 – 3 = 2 x 3𝓍

⇒ 8𝓍 – 3 = 6𝓍

⇒ 8𝓍 – 6𝓍 = 3

⇒ 2𝓍 = 3

⇒ 𝓍 = ³⁄₂

Question: 2. Solve :

Answer :

Mddle block 1

⇒ 9𝓍 = 15(7 – 6𝓍)

⇒ 9𝓍 = 105 – 90𝓍

⇒ 9𝓍 + 90𝓍 = 105

⇒ 99𝓍 = 105

⇒ 𝓍 = ¹⁰⁵⁄₉₉

⇒ 𝓍 = ³⁵⁄₃₃

Question: 3. Solve :

Answer :

⇒ z x 9 = 4(z + 15)

⇒ 9z = 4z + 60

⇒ 9z – 4z = 60

⇒ 5z = 60

⇒ z = 12

Question: 4. Solve :

Answer :

⇒ 5(3y + 4) = -2(2 – 6y)

⇒ 15y + 20 = -4 + 12y

⇒ 15y – 12y = -4 – 20

⇒ 3y = -24

⇒ y = -8

Question: 5. Solve :

Answer :

⇒ 3(7y + 4) = -4(y + 2)

⇒ 21y + 12 = -4y – 8

⇒ 21y + 4y = -8 – 12

⇒ 25y = -20

⇒ y = ^-20⁄₂₅

⇒ y = ^-4⁄₅

Question: 6. The ages of Hari and Harry are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. Find their present ages.

Answer :
Let the Ages of Hari and Harry be 5𝓍 years and 5𝓍 years.

According to question,

⇒ 4(5𝓍 + 4) = 3(7𝓍 + 4)
⇒ 20𝓍 + 16 = 21𝓍 + 12
⇒ 20𝓍 – 21𝓍 = 12 – 16
⇒ -𝓍 = -4
⇒ 𝓍 = 4
Hence, the age of Hari = 5𝓍 = 5 x 4
= 20 years
And the age of Harry = 7𝓍 = 7 x 4
= 28 years.
Question: 7. The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is ³⁄₂ Find the rational number.
Answer :
Let the numerator of a rational number be 𝓍 then the denominator is 𝓍 + 8.
Therefore, Rational number =
According to the question,

⇒ 2(𝓍 + 17) = 3(𝓍 + 7)

⇒ 2𝓍 + 34 = 3𝓍 + 21

⇒ 2𝓍 – 3𝓍 = 21 – 34

⇒ -𝓍 = -13

⇒ 𝓍 = 13

Hence, the required rational number

Bottom Block 3