If 2x+7 5 − 3x+11 2 = 2x+8 3 −5 , then the value of x is [[1]].

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If $\frac{2 x + 7}{5} - \frac{3 x + 11}{2} = \frac{2 x + 8}{3} - 5$ , then the value of $x$ is [[1]].

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answer is -1.

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Detailed Solution

The value of x in the equation

\frac{2 x + 7}{5} - \frac{3 x + 11}{2} = \frac{2 x + 8}{3} - 5

, so that the equation holds true is -1.
The linear equation is as follows,

\frac{2 x + 7}{5} - \frac{3 x + 11}{2} = \frac{2 x + 8}{3} - 5

Proceeding with solving the equation, 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 3, i.e., 30.
So, multiplying each side of the given equation by 30 and simplifying it, we get,

\frac{30 (2 x + 7)}{5} - \frac{30 (3 x + 11)}{2} = \frac{30 (2 x + 8)}{3} - (5 \times 30)

6 (2 x + 7) - 15 (3 x + 11) = 10 (2 x + 8) - 150

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

(6 \times 2 x) + (6 \times 7) - (15 \times 3 x) - (15 \times 11) = (10 \times 2 x) + (10 \times 8) - 150

12 x + 42 - 45 x - 165 = 20 x + 80 - 150

Now, adding the like terms together, the above equation can be written as follows,

- 33 x - 123 = 20 x - 70

Next, we will transpose the variable terms to the left and constants to the right side of the equality by adding 123 and subtracting 20x on each side of the above equation as follows,