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CTET Paper II (Mathematics and Science) 31 Dec 2021 Solved Paper

Question : 48 of 150

Marks: +1, -0

\frac{3x-4}{3}+\frac{2x+1}{2}=x+\frac{7}{6}

\frac{5x-1}{4}

is:

Solution:

Concept:

Solve a linear equation by clearing denominators and simplifying.

Explanation:

Start with the equation:

\frac{3x-4}{3}+\frac{2x+1}{2}=x+\frac{7}{6}

Multiply both sides by the LCM of 3, 2, and 6, which is 6.

2(3x-4) + 3(2x+1) = 6x + 7

Expand:

6x - 8 + 6x + 3 = 6x + 7

Combine like terms:

12x - 5 = 6x + 7

Subtract

6x

from both sides:

6x - 5 = 7

Add 5:

6x = 12

x = 2

Now substitute into

\frac{5x-1}{4}

\frac{5(2)-1}{4} = \frac{10-1}{4} = \frac{9}{4}

Answer:

\frac{9}{4}

, which is option A.

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