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

Question

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

Accepted Answer

The value of x in the equation                2x+7    5      −         3x+11    2      =         2x+8    3      −5 , so that the equation holds true is -1.The linear equation is as follows,               2x+7    5      −         3x+11    2      =         2x+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,                30(2x+7)    5      −         30(3x+11)    2      =         30(2x+8)    3      −(5×30)       6(2x+7)−15(3x+11)=10(2x+8)−150 Now, using the distributive property of multiplication, the equation can be simplified as follows,      (6×2x)+(6×7)−(15×3x)−(15×11)=(10×2x)+(10×8)−150                                              12x+42−45x−165=20x+80−150 Now, adding the like terms together, the above equation can be written as follows,      −33x−123=20x−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,               −33x−20x−123+123=20x−20x−70+123                   −53x=53                               Now, we will divide each side by -53 to get the value of the variable as follows,                            −53x             −53          =             53             −53                             x=−1            Thus, x= -1 is the required value.

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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