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Exercise 2.6 - Chapter 2 Linear Equations In One Variable class 8 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Solve: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3075/Chapter%202_html_617e8022.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3075/Chapter%202_html_617e8022.gif

On multiplying both sides by 3x, we obtain

8x − 3 = 6x

⇒ 8x − 6x = 3

⇒ 2x = 3

⇒ https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3075/Chapter%202_html_m6f1b144a.gif

Question 2:

Solve: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3078/Chapter%202_html_m759c533.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3078/Chapter%202_html_m759c533.gif

Onmultiplying both sides by 7 − 6x, we obtain

9x = 15(7 − 6x)

⇒ 9x = 105 − 90x

⇒ 9x + 90x = 105

⇒ 99x = 105

⇒ https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3078/Chapter%202_html_m22082180.gif

Question 3:

Solve: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3083/Chapter%202_html_2b745f32.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3083/Chapter%202_html_2b745f32.gif

On multiplying both sides by 9(z + 15), we obtain

9= 4(z + 15)

⇒ 9= 4z + 60

⇒ 9− 4z = 60

⇒ 5z = 60

⇒ z = 12

Question 4:

Solve: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3084/Chapter%202_html_682fc34d.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3084/Chapter%202_html_m10eac5da.gif

On multiplying both sides by 5(2 − 6y), we obtain

5(3y + 4) = −2(2 − 6y)

⇒ 15y + 20 = − 4 + 12y

⇒ 15y − 12y = − 4 − 20

⇒ 3y = −24

⇒ y = −8

Question 5:

Solve: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3086/Chapter%202_html_1a3bbc06.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3086/Chapter%202_html_m66f57e8a.gif

On multiplying both sides by 3(+ 2), we obtain

3(7y + 4) = −4(y + 2)

⇒ 21y + 12 = − 4y − 8

⇒ 21y + 4y = − 8 − 12

⇒ 25y = −20

⇒ https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3086/Chapter%202_html_m642245e5.gif

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 common ratio between their ages be x. Therefore, Hari’s age and Harry’s age will be 5x years and 7x years respectively and four years later, their ages will be (5x + 4) years and (7x + 4) years respectively.

According to the situation given in the Question,

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3088/Chapter%202_html_m357f13b2.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3088/Chapter%202_html_3b81c7d5.gif

Hari’s age = 5x years = (5 × 4) years = 20 years

Harry’s age = 7x years = (7 × 4) years = 28 years

Therefore, Hari’s age and Harry’s age are 20 years and 28 years respectively.

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 ishttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3091/Chapter%202_html_m47d40970.gif . Find the rational number.

Answer:

Let the numerator of the rational number be x. Therefore, its denominator will

be x + 8.

The rational number will behttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3091/Chapter%202_html_546cec9c.gif . According to the Question,

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3091/Chapter%202_html_m381eba82.gif

⇒ 2(x + 17) = 3(x + 7)

⇒ 2x + 34 = 3x + 21

⇒ 34 − 21 = 3x − 2x

⇒13 = x

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/3091/Chapter%202_html_m695f782e.gif

Also Read : Exercise-3.1-Chapter-3-Understanding-Quadrilaterals-class-8-ncert-solutions-Maths

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