NCERT Solutions for Class 8 Maths Chapter 2: Linear Equations in One Variable - Exercise 2.6

1. Find the solution of \[\frac{\text{8x-3}}{\text{3x}}\text{=2}\]

Ans: We have an equation \[\frac{\text{8x-3}}{\text{3x}}\text{=2}\]

Multiplying both sides by \[\text{3x}\]

\[\Rightarrow \text{8x-3=6x}\]

Shifting \[\text{6x}\] to left side and \[\text{3}\] to right side

\[\Rightarrow \text{8x-6x=3}\]

\[\Rightarrow \text{2x=3}\]

Dividing both sides by \[\text{2}\]

\[\Rightarrow \text{x=}\frac{\text{3}}{\text{2}}\]

2. Find the solution of \[\frac{\text{9x}}{\text{7-6x}}\text{=15}\]

Ans: We have an equation \[\frac{\text{9x}}{\text{7-6x}}\text{=15}\]

Multiplying both sides by \[\text{7-6x}\]

\[\Rightarrow \text{9x=15}\left( \text{7-6x} \right)\]

\[\Rightarrow \text{9x=105-90x}\]

Shifting \[\text{90x}\] to left side 

\[\Rightarrow \text{9x+90x=105}\]

\[\Rightarrow \text{99x=105}\]

Dividing both sides by \[\text{99}\]

\[\Rightarrow \text{x=}\frac{\text{105}}{\text{99}}\]

\[\Rightarrow \text{x=}\frac{\text{35}}{\text{33}}\]

3. Find the solution of \[\frac{\text{z}}{\text{z+15}}\text{=}\frac{\text{15}}{\text{9}}\]

Ans: We have an equation \[\frac{\text{z}}{\text{z+15}}\text{=}\frac{\text{4}}{\text{9}}\]

Multiplying both sides by \[9\left( \text{z+15} \right)\]

\[\Rightarrow \text{9z=4}\left( \text{z+15} \right)\]

\[\Rightarrow \text{9z=4z+60}\]

Shifting \[\text{4z}\] to left side 

\[\Rightarrow \text{9z-4z=60}\]

\[\Rightarrow \text{5z=60}\]

Dividing both sides by \[\text{5}\]

\[\Rightarrow \text{z=12}\]

4. Find the solution of \[\frac{\text{3y+4}}{\text{2-6y}}\text{=}\frac{\text{-2}}{\text{5}}\]

Ans: We have an equation \[\frac{\text{3y+4}}{\text{2-6y}}\text{=}\frac{\text{-2}}{\text{5}}\]

Multiplying both sides by \[\text{5}\left( \text{2-6y} \right)\]

\[\Rightarrow \text{5}\left( \text{3y+4} \right)\text{=-2}\left( \text{2-6y} \right)\]

\[\Rightarrow \text{15y+20=-4+12y}\]

Shifting \[\text{12y}\] to left side and \[\text{20}\] to right side 

\[\Rightarrow \text{15y-12y=-4-20}\]

\[\Rightarrow \text{3y=-24}\]

Dividing both sides by \[\text{3}\]

\[\Rightarrow \text{y=-8}\]

5. Find the solution of \[\frac{\text{7y+4}}{\text{y+2}}\text{=}\frac{\text{-4}}{\text{3}}\]

Ans: We have an equation \[\frac{\text{7y+4}}{\text{y+2}}\text{=}\frac{\text{-4}}{\text{3}}\]

Multiplying both sides by \[\text{3}\left( \text{y+2} \right)\]`

\[\Rightarrow \text{3}\left( \text{7y+4} \right)\text{=-4}\left( \text{y+2} \right)\]

\[\Rightarrow \text{21y+12=-4y-8}\]

Shifting \[\text{4y}\] to left side and \[\text{12}\] to right side 

\[\Rightarrow \text{21y+4y=-8-12}\]

\[\Rightarrow \text{25y=-20}\]

Dividing both sides by \[\text{25}\]

\[\Rightarrow \text{y=}\frac{\text{-20}}{\text{25}}\]

\[\Rightarrow \text{y=-}\frac{\text{4}}{\text{5}}\]

6. The ages of Hari and Harry are in the ratio \[\text{5:7}\]. Four years from now the ratio of their ages will be \[\text{3:4}\]. Find their present ages.

Ans: Let us assume the ratio be \[\text{x}\], therefore,

Age of Hari will be \[\text{5x}\] years and age of Harry be \[\text{7x}\] years,

Age of Hari after four years will be \[\text{5x+4}\] years and age of Harry after four years will be \[\text{7x+4}\]

Now,

\[\Rightarrow \frac{\text{5x+4}}{\text{7x+4}}\text{=}\frac{\text{3}}{\text{4}}\]

Multiplying both sides by \[\text{4}\left( \text{7x+4} \right)\]`

\[\Rightarrow \text{4}\left( \text{5x+4} \right)\text{=3}\left( \text{7x+4} \right)\]

\[\Rightarrow \text{20x+16=21x+12}\]

Shifting \[\text{12}\] to left side and \[\text{20x}\] to right side 

\[\Rightarrow \text{16-12=21x-20x}\]

\[\Rightarrow \text{x=4}\]

Therefore, age of Hari is \[\text{5x}\Rightarrow \text{20}\] years and age of Harry is \[\text{7x}\Rightarrow \text{28}\] years.

7. The denominator of a rational number is greater than its numerator by \[\text{8}\]. If the numerator is increased by \[\text{17}\] and the denominator is decreased by \[\text{1}\], the number obtained is \[\frac{\text{3}}{\text{2}}\]. Find the rational number.

Ans: Let us assume the rational number be \[\text{x}\], therefore, the denominator will be \[\text{x+8}\], hence, the rational number would be \[\frac{\text{x}}{\text{x+8}}\] 

According to the question,

\[\Rightarrow \frac{\text{x+17}}{\text{x+8-1}}\text{=}\frac{\text{3}}{\text{2}}\]

\[\Rightarrow \frac{\text{x+17}}{\text{x+7}}\text{=}\frac{\text{3}}{\text{2}}\]

Multiplying both sides by \[\text{2}\left( \text{x+7} \right)\]`

\[\Rightarrow \text{2}\left( \text{x+17} \right)\text{=3}\left( \text{x+7} \right)\]

\[\Rightarrow \text{2x+34=3x+21}\]

Shifting \[\text{21}\] to left side and \[\text{2x}\] to right side 

\[\Rightarrow \text{34-21=3x-2x}\]

\[\Rightarrow \text{x=13}\]

Denominator \[\left( \text{x+8} \right)\text{=21}\]

Therefore, the rational number would be \[\frac{13}{21}\].

Introduction to Class 8 Maths Chapter 2 Exercise 2.6:

Linear Equations applies one or more variables where one variable is dependent on another. Wherever you see an unknown quantity, it can be represented as a linear equation. For example, you can calculate the mileage rates, predict profits, find out income overtime rate, and a lot more in your day to day life with the assistance of a linear equation.

However, learning linear equations can be tricky that needs concentration with proper understanding. Still, Vedantu makes learning more natural with the easy to grasp formulas and methods provided into the NCERT solutions for Class 8 Maths Chapter 2 Exercise 2.6.

Why You Need NCERT Solution Of Class 8 Maths Chapter 2 Exercise 2.6

Solving Linear Equations for One Variable can be easier at the beginning, but with the increased complexity, it can also tend to be complicated. Hence, you need to practice and understand every question examined precisely to help you in the long run. Therefore we have prepared all the solutions keeping the shortest method into consideration.

Advantages of Maths NCERT Solutions Class 8 Chapter 2 Exercise 2.6

Linear Equations can be lengthy to solve at times. But explaining it in a smart and precise way is what we do at Vedantu. Having years of expertise in the field, our teachers have crafted solutions for every query in the shortest method possible. What's more? With NCERT Solutions for Class 8 Maths Chapter 2 Exercise 2.6, you can get a precise knowledge and understanding of the chapter. So what are you thinking of yet? Download the PDF today and start solving the toughest questions with the most straightforward methods. 

Quality Of NCERT Solutions Of Class 8 Maths Chapter 2 Exercise 2.6:

Offering our students quality solutions and study material is what we do at Vedantu. We believe in giving them the best possible method of teaching we can. Our teachers have years of expertise in solving Linear Equations of all aspects - hence, you don't need to worry about what you get.

Experts having years of Industry Experience:

Having years of expertise in the field, we know what it takes to deliver the best methods and solutions to the students that can help them to get ahead and achieve miles to success. Our answers and teaching methods are crafted in such a way that anyone can understand it in no time.

Solved Queries of Class 8 Maths Chapter 2 Exercise 2.6 For Free:

Worried about the amount of money you will have to pay for solutions from Vendantu? You do not have to, because you can download the PDF available online for free. We do not have any hidden charges, just one click, and you have everything you need.

Everything As Per NCERT Guidelines:

All the solutions provided by our teachers are for Class 8 Maths Chapter 2 Exercise 2.6 is 100% as per the NCERT guidelines. Hence, you can rely on them without scratching your head and pass your exams with flying colours.

How Vedantu's NCERT Solution Can Help You to Study and Learn in Easy Way?

Learning has transformed since the boost of the digital age, and Vedantu has proved to be the one prominent pioneer in facilitating students with better solutions each day. From an easy to use a mobile application to offering students’ potential solutions to score well in exams - it has proved to be a helping hand for them. What's more? Everything provided by Vedantu considers the precise methodologies so that every student can understand it with the perfect depth and remembers for years and years to come. 

So if you are someone looking for quick and easy NCERT Solutions for Class 8th Maths Chapter 2 Exercise 2.6 - Download PDF offered by Vedantu today!