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CTET Paper II (Mathematics and Science) 7 Feb 2026 Shift 1 Solved Paper

Question : 33 of 150

Marks: +1, -0

\frac{7x-1}{4} - \frac{1}{3} \left( 2x - \frac{1-x}{2} \right) = \frac{10}{3}

\frac{11x+21}{2}

Solution:

Concept:

Simplify complex linear equations by first handling the inner bracket, then clearing denominators to solve for

x

Explanation:

First, simplify inside the bracket:

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

Now the equation becomes:

\frac{7x-1}{4} - \frac{1}{3} \cdot \frac{5x-1}{2} = \frac{10}{3}

This simplifies to:

\frac{7x-1}{4} - \frac{5x-1}{6} = \frac{10}{3}

Multiply every term by the LCM 12:

3(7x-1) - 2(5x-1) = 40

Expand:

21x - 3 - 10x + 2 = 40

Combine like terms:

11x - 1 = 40

Solve:

11x = 41

, so

x = \frac{41}{11}

Now find

\frac{11x+21}{2} = \frac{41 + 21}{2} = \frac{62}{2} = 31

Answer:

B. 31

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