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CTET Paper II (Mathematics and Science) 17 Jan 2022 Solved Paper

Question : 38 of 150

Marks: +1, -0

5x-6(x+\frac{1}{30})=\frac{1}{3}(x+1)

(5x+6)

Solution:

Concept:

Solve a linear equation in one variable by simplifying and isolating

x

, then substitute to find the required expression.

Explanation:

Start with

5x - 6(x + \frac{1}{30}) = \frac{1}{3}(x + 1)

Expand:

5x - 6x - \frac{6}{30} = \frac{x}{3} + \frac{1}{3}

Simplify:

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

Bring

x

terms to left, constants to right:

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

Combine:

-\frac{4x}{3} = \frac{5+3}{15} = \frac{8}{15}

Multiply both sides by

-\frac{3}{4}

x = -\frac{8}{15} \times \frac{3}{4} = -\frac{2}{5}

Now compute

5x + 6 = 5 \times (-\frac{2}{5}) + 6 = -2 + 6 = 4

Answer:

Option B. 4

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