Download App

Linear Equations in One Variable — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsLinear Equations in One Variable5 Marks
Question
Solve the following equation and verify your answer:
$\frac{\text{x}^2-(\text{x}+1)(\text{x}+2)}{5\text{x}+1}=6$
✓

Answer

$\frac{\text{x}^2-(\text{x}+1)(\text{x}+2)}{5\text{x}+1}=\frac{6}{1}$
$\Rightarrow\frac{\text{x}^2-(\text{x}^2+2\text{x}+\text{x}+2)}{5\text{x}+1}=\frac{6}{1}$
$\Rightarrow\frac{\text{x}^2-\text{x}^2-2\text{x}-\text{x}-2}{5\text{x}+1}=\frac{6}{1}$
$\Rightarrow\frac{-3\text{x}-2}{5\text{x}+1}=\frac{6}{1}$
By cross multiplication:
$-3\text{x}-2=6(5\text{x}+1)$
$\Rightarrow-3\text{x}-2=30\text{x}+6$
$\Rightarrow-3\text{x}-30=6+2$
(By transposition)
$\Rightarrow-33\text{x}=8$
$\Rightarrow\text{x}=\frac{8}{-33}$
$=\frac{-8}{33}$
$\therefore\text{x}=\frac{-8}{33}$
Verification:
$\text{L.H.S.}=\frac{\text{x}^2-(\text{x}+1)(\text{x}+2)}{5\text{x}+1}$
$=\frac{\Big(\frac{-8}{33}\Big)^2-\Big(\frac{-8}{33}+1\Big)\Big(\frac{-8}{33}+2\Big)}{\Big(\frac{-8}{33}\Big)+1}$
$=\frac{\frac{64}{1089}-\Big(\frac{25}{33}\times\frac{58}{33}\Big)}{\frac{-40+33}{33}}$
$=\frac{\frac{64}{1089}-\frac{1450}{1089}}{\frac{-7}{33}}=\frac{\frac{64-1450}{1089}}{\frac{-7}{33}}$
$=\frac{-1386}{1089}\times\frac{33}{-7}=6=\text{R.H.S.}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Mark Question" from Linear Equations in One Variable→Linear Equations in One Variable — all question types→Maths STD 8 question papers→Maharashtra Board STD 8 question papers→Maharashtra Board question paper generator→

Similar questions

The following table shows how a student spends his pocket money during the course of a month. Represent it by a pie-diagram.
Items
Food
Entertainment
Other expenditure
Savings
Expenditure
40%
25%
20%
15%
→
The weights of new born babies (in kg) in a hospital on a particular day are as follows:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4.
  1. Rearrange the weights in descending order.
  2. Determine the highest weight.
  3. Determine the lowest weight.
  4. Determine the range.
  5. How many babies were born on that day?
  6. How many babies weigh below 2.5 kg?
  7. How many babies weigh more than 2.8 kg?
  8. How many babies weigh 2.8 kg?
→
x varies inversely as y, when x = 15 then y = 10, if x = 20, then y = ?
→
A dealer sold a camera for Rs. 1080 gaining $\frac{1}{8}$ of its cost price. Find (i) the cost price of the camera, and (ii) the gain percent earned by the dealer.
→
The following table shows the percentage of students who dropped out of school after completing high school.
Year
2005
2007
2009
2011
2013
2015
2017
Percentage of students who dropped out of school
6%
5.5%
5%
4.7%
4.9%
4%
4.5%
Study the above table carefully and draw a line graph to depict it.
→
Rakesh goes to a departmental store and purchases the following article:
  1. Biscuits and bakery products costing Rs. 50, VAT @ 5%.
  2. Medicine costing Rs. 90, VAT @ 10%.
  3. Clothes costing Rs 400, VAT @ 1%.
  4. Cosmetic Rs. 150, VAT @ 10% Calculate the total amount to be paid by Rakesh to the store.
→
Resolve of the folloeing quadratic equation trinomials into factor:
$(2 a-b)^2+(2 a-b)-8$
→
In one day the sales (in rupees) of different items of a baker's shop are given below:
Items
 Ordinary bread Fruit bread Cakes and Pastries Biscuits Others Total
Sales (in Rs.)
260
40
100
60
 20
480
Draw a pie-chart representing the above sales.
→
Following is the break up of the expenditure of a family on different items of consumption:
Items
Food
Clothing
Rent
Education
Fuel etc.
Medicine
Miscellaneous
Expenditure (in Rs.)
1600
200
600
150
100
80
270
Draw a pie-diagram to represent the above data.
→
Solve the following equation and also check your result in case:
$\frac{7\text{x}-1}{4}-\frac{1}{3}\Big(2\text{x}-\frac{1-\text{x}}{2}\Big)=\frac{10}{3}$
→