If x−5 2 − x−3 5 = 1 2 , then the value of x is [[1]].

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If $\frac{x - 5}{2} - \frac{x - 3}{5} = \frac{1}{2}$ , then the value of $x$ is [[1]].

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answer is 8.

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Detailed Solution

The value of x in the equation

\frac{x - 5}{2} - \frac{x - 3}{5} = \frac{1}{2}

, so that it is a true equation is 8.
We have the linear equation as follows,

\frac{x - 5}{2} - \frac{x - 3}{5} = \frac{1}{2}

.
We first need to eliminate the denominators on both sides of the equation.
To do so, we will have to look for the LCM of 5, 2 and 2, i.e., 10.
So, multiplying each side of the given equation by 10 and simplifying it, we get,

\begin{array}{l} (10 \times \frac{x - 5}{2}) - (10 \times \frac{x - 3}{5}) = \frac{1}{2} \times 10 \\ 5 (x - 5) - 2 (x - 3) = 5 \end{array}

Now, using the distributive property of multiplication, the equation can be simplified as follows,

\begin{array}{l} 5 (x) + 5 (- 5) - 2 \times (x) - 2 (- 3) = 5 \\ \Rightarrow 5 x - 25 - 2 x + 6 = 5 \end{array}

\Rightarrow 3 x - 19 = 5

\Rightarrow 3 x = 24

Dividing by 3 on both sides, we get,

\begin{array}{l} \frac{3 x}{3} = \frac{24}{3} \\ x = 8 \end{array}

Thus, x = 8 is the required value.

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