Download App

Linear Equations in One Variable — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsLinear Equations in One Variable4 Marks
Question
Solve the following equations. Check your result in case.
$\frac{2\text{x}-3}{5}+\frac{\text{x}+3}{4}=\frac{4\text{x}+1}{7}$
✓

Answer

$\frac{2\text{x}-3}{5}+\frac{\text{x}+3}{4}=\frac{4\text{x}+1}{7}$
$\frac{28(2\text{x}-3)+35(\text{x}+3)=20(4\text{x}+1)}{140}$ (LCM of 5, 4, 7 = 140)
$28(2\text{x}-3)+35(\text{x}+3)=20(4\text{x}+1)$
$\Rightarrow56\text{x}-84+35\text{x}+105=80\text{x}+20$
$\Rightarrow56\text{x}+35\text{x}-80\text{x}=20+84-105$
$\Rightarrow91\text{x}-80\text{x}=140-105$
$\Rightarrow11\text{x}=-1$
$\Rightarrow\text{x}=\frac{-1}{11}$
$\therefore\text{x}=\frac{-1}{11}$
Check:
$\text{L.H.S.}=\frac{2\text{x}-3}{5}+\frac{\text{x}+3}{4}$
$=\frac{2\Big(-\frac{1}{11}\Big)-3}{5}+\frac{\frac{-1}{11}+3}{4}$
$=\frac{\frac{-2}{11}-3}{5}+\frac{\frac{-1}{11}+3}{4}$
$=\frac{-2-33}{11\times5}+\frac{-1+33}{11\times4}$
$=\frac{-35}{11\times5}+\frac{32}{11\times4}$
$=\frac{-7}{11}+\frac{8}{11}$
$=\frac{1}{11}$
$\text{R.H.S}.=\frac{4\text{x}+1}{7}$
$=\frac{4\Big(-\frac{1}{11}\Big)+1}{7}$
$=\frac{-\frac{4}{11}+1}{7}$
$=\frac{-4+11}{11\times7}$
$=\frac{7}{11\times7}$
$=\frac{1}{11}$
$\text{L.H.S. = R.H.S.}$

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 "4 Mark Question" from Linear Equations in One Variable→Linear Equations in One Variable — all question types→Maths STD 7 question papers→Maharashtra Board STD 7 question papers→Maharashtra Board question paper generator→

Similar questions

In a $\triangle \text{ABC},$ AD is the altitude from A such that AD = 12cm. BD = 9cm and DC = 16cm. Examine if $\triangle \text{ABC},$ is right angled at A.
→
A dice is thrown 100 times and the outcomes are noted as given below:
Outcome
1
2
3
4
5
6
Frequency
21
14
18
15
23
9
When a dice is thrown at random, what is the probability of getting a (i) 3, (ii) 6, (iii) 6, (iv) 1?
→
How much does $a^2-3 a b+2 b^2$ exceed $2 a^2-7 a b+9 b^2$ ?
→
Solve the following equations. Check your result in case.
$\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}=\frac{1}{3}$
→
Evaluate:
$\frac{-16}{9}+\frac{-5}{12}+\frac{7}{18}$
→
The ratio of the radii of two circles is $4: 5$. Find the ratio of their areas.
→
Write five examples of each one of:
  1. A cone.
  2. A sphere.
  3. A cuboid.
  4. A cylinder.
→
$0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
→
Students of a certain school went for a picnic to a farm by bus. Here are some of their experiences. Say whether the quantities in each are in direct or in inverse proportion.

i. Each student paid Rs 60 for the expenses.
As there were 45 students,___rupees were collected.
Had there been 50 students,___rupees would have been collected.
The number of students and money collected are in___proportion.

ii. The sweets shop near the school gave 90 laddoos for the picnic.
If 45 students go for the picnic, each will get___laddoos.
If 30 students go for the picnic, each will get___laddoos.
The number of students and that of laddoos each one gets are in___proportion.

iii. The farm is 120 km away from the school.
The bus went to the farm at a speed of 40 km per hour and took___hours.
On the return trip, the speed was 60 km per hour. Therefore, it took___hours.
The speed of the bus and the time it takes are in___proportion.

iv. The farmer picked 180 bors from his trees.
He gave them equally to 45 students. Each student got___bors.
Had there been 60 students, each would have got___bors.
The number of students and the number of bors each one gets are in___proportion.

→
Draw $\triangle\text{ABC}$ in which AC = 6cm, $\angle\text{A}=90^\circ$ and $\angle\text{B}=60^\circ.$
→