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CTET Paper II (Mathematics and Science) 15 Dec 2024 Shift 1 Solved Paper

Question : 55 of 150

Marks: +1, -0

\frac{7x-1}{4}-\frac{1}{7}(2x-\frac{1-x}{2})=4

\frac{5x-3}{3x-1}

Solution:

Concept:

Simplify the given linear equation to find the value of

x

, then substitute it into the required expression.

Explanation:

First, simplify the inner bracket:

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

Substitute back:

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

This gives

\frac{7x-1}{4} - \frac{5x-1}{14} = 4

Find a common denominator (28):

\frac{49x-7}{28} - \frac{10x-2}{28} = 4

Combine:

\frac{49x-7 - (10x-2)}{28} = \frac{39x-5}{28} = 4

Multiply both sides by 28:

39x - 5 = 112

39x = 117

, hence

x = 3

Now evaluate

\frac{5x-3}{3x-1} = \frac{5(3)-3}{3(3)-1} = \frac{15-3}{9-1} = \frac{12}{8} = \frac{3}{2}

Answer:

\frac{3}{2}

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