Question
Solve:
$\frac{\text{2x}+7}{5}-\frac{\text{3x}+11}{2}=\frac{2\text{x}+8}{3}-5$
$\frac{\text{2x}+7}{5}-\frac{\text{3x}+11}{2}=\frac{2\text{x}+8}{3}-5$
✓
Answer
$\frac{\text{2x}+7}{5}-\frac{\text{3x}+11}{2}=\frac{2\text{x}+8}{3}-5$
$\Rightarrow\frac{2\text{x} + 7}{5} - \frac{3\text{x} + 11}{2} = \frac{2\text{x} + 8 - 15}{3} $ (L.C.M of 3 and 1 is 3)
$\Rightarrow30\Big(\frac{2\text{x} + 7}{5}\Big) -30\Big( \frac{3\text{x} + 11}{2}\Big) =30\Big( \frac{2\text{x} + 8 - 15}{3} \Big)$
(multiplying throughout by 30, which is the L.C.M. of 5, 2 and 3)
$\Rightarrow6 (2\text{x} + 7) - 15 (3\text{x} + 11) = 10 (2\text{x} + 8 - 15) $
$\Rightarrow12\text{x} + 42 -45\text{x} - 165 = 20\text{x} - 70$
$-33\text{x}-123=20\text{x}$
$\Rightarrow\frac{2\text{x} + 7}{5} - \frac{3\text{x} + 11}{2} = \frac{2\text{x} + 8 - 15}{3} $ (L.C.M of 3 and 1 is 3)
$\Rightarrow30\Big(\frac{2\text{x} + 7}{5}\Big) -30\Big( \frac{3\text{x} + 11}{2}\Big) =30\Big( \frac{2\text{x} + 8 - 15}{3} \Big)$
(multiplying throughout by 30, which is the L.C.M. of 5, 2 and 3)
$\Rightarrow6 (2\text{x} + 7) - 15 (3\text{x} + 11) = 10 (2\text{x} + 8 - 15) $
$\Rightarrow12\text{x} + 42 -45\text{x} - 165 = 20\text{x} - 70$
$-33\text{x}-123=20\text{x}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Construct ₹PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°. If it is given that ₹PQRS is a parallelogram, which of the given information is unnecessary ?
Find the area enclosed by the following figures as the sum of the areas of a rectangle and a trapezium:
By what number should the following numbers be multiplied to get a perfect square in each case? Also, find the number whose square is the new number.
3675
3675
Gunpowder contains 75% nitre and 10% sulphur. Find the amount of the gunpowder which carrier 9kg nitre. What amount of gunpowder would contain 2.3kg sulphur?
By what numbers should the following be divided to get a perfect square in case? Also, find the number whose square is the new number.
3698
3698
A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring $22 cm \times 12.5 cm \times 7.5 cm$. If $\frac{1}{12}$ of the total volume of the wall consists of mortar, how many bricks are there in the wall?
→Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.
The area of a square field is $60025 m^2$. A man cycles along its boundary at $18 km / hr$. In how much time will he return at the starting point?
→Simplify : $\frac{x^2-5 x-24}{(x+3)(x+8)} \times \frac{x^2-64}{(x-8)^2}$
→Find three rational numbers between 4 and 5.