Class 8 - Mathematics
Linear Equations in One Variable - Exercise 2.6
Top Block 1
Solve the following equations.
Question: 1. Solve :
Answer :
⇒ 8𝓍 – 3 = 6𝓍
⇒ 8𝓍 – 6𝓍 = 3
⇒ 2𝓍 = 3
⇒ 𝓍 = 3⁄2
Question: 2. Solve :
Answer :
Mddle block 1
⇒ 9𝓍 = 105 – 90𝓍
⇒ 9𝓍 + 90𝓍 = 105
⇒ 99𝓍 = 105
⇒ 𝓍 = 105⁄99
⇒ 𝓍 = 35⁄33
Question: 3. Solve :
Answer :
⇒ 9z = 4z + 60
⇒ 9z – 4z = 60
⇒ 5z = 60
⇒ z = 12
Question: 4. Solve :
Answer :
⇒ 15y + 20 = -4 + 12y
⇒ 15y – 12y = -4 – 20
⇒ 3y = -24
⇒ y = -8
Question: 5. Solve :
Answer :
⇒ 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,
⇒ 2𝓍 + 34 = 3𝓍 + 21
⇒ 2𝓍 – 3𝓍 = 21 – 34
⇒ -𝓍 = -13
⇒ 𝓍 = 13
Hence, the required rational number
