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CTET Paper II (Mathematics and Science) 20 Dec 2021 Solved Paper

Question : 38 of 150

Marks: +1, -0

If 4 –

\frac{2(x - 4)}{3}=\frac{1}{2}

\frac{2x + 1}{2}

is equal to

Solution:

Concept:

Solve the linear equation using algebraic operations to find

x

, then substitute into the given expression.

Explanation:

Start with:

4 - \frac{2(x-4)}{3} = \frac{1}{2}(2x+5)

Multiply both sides by 6 (LCM of 2 and 3):

24 - 4(x-4) = 3(2x+5)

Simplify:

24 - 4x + 16 = 6x + 15

, so

40 - 4x = 6x + 15

Bring terms:

40 - 15 = 6x + 4x

, i.e.,

25 = 10x

Thus

x = \frac{25}{10} = \frac{5}{2} = 2.5

Now evaluate

\frac{2x+1}{2}

: substitute

x = \frac{5}{2}

\frac{2 \times \frac{5}{2} + 1}{2} = \frac{5+1}{2} = \frac{6}{2} = 3

Answer:

3

(Option C)

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