Solve the linear equation 1 4 x + 2 = 6 7 x − 3 \frac { 1 } { 4 } x + 2 = \frac { 6 } { 7 } x - 3 4 1 x + 2 = 7 6 x − 3 for x .A) x = 140 17 x = \frac { 140 } { 17 } x = 17 140 B) x = − 140 17 x = - \frac { 140 } { 17 } x = − 17 140 C) x = 28 17 x = \frac { 28 } { 17 } x = 17 28 D) x = − 28 17 x = - \frac { 28 } { 17 } x = − 17 28 E) there is no solution

Question

Solve the linear equation   1 4 x + 2 = 6 7 x − 3 \frac { 1 } { 4 } x + 2 = \frac { 6 } { 7 } x - 3 4 1 ​ x + 2 = 7 6 ​ x − 3   for x .A)    x = 140 17 x = \frac { 140 } { 17 } x = 17 140 ​ B)    x = − 140 17 x = - \frac { 140 } { 17 } x = − 17 140 ​ C)    x = 28 17 x = \frac { 28 } { 17 } x = 17 28 ​ D)    x = − 28 17 x = - \frac { 28 } { 17 } x = − 17 28 ​ E) there is no solution

Zybrea Knight · Accepted Answer

Final Answer : A, Explanation :   To solve the equation   1 4 x + 2 = 6 7 x − 3 \frac { 1 } { 4 } x + 2 = \frac { 6 } { 7 } x - 3 4 1 ​ x + 2 = 7 6 ​ x − 3  , first get all the x terms on one side and the constants on the other. Subtract   1 4 x \frac { 1 } { 4 } x 4 1 ​ x   from both sides and add 3 to both sides to get   5 = 6 7 x − 1 4 x 5 = \frac { 6 } { 7 } x - \frac { 1 } { 4 } x 5 = 7 6 ​ x − 4 1 ​ x  . To combine the x terms, find a common denominator, which is 28, leading to   5 = 24 28 x − 7 28 x 5 = \frac { 24 } { 28 } x - \frac { 7 } { 28 } x 5 = 28 24 ​ x − 28 7 ​ x  , simplifying to   5 = 17 28 x 5 = \frac { 17 } { 28 } x 5 = 28 17 ​ x  . Solving for x gives   x = 140 17 x = \frac { 140 } { 17 } x = 17 140 ​  .

Solve the linear equation $14x+2=67x−3\frac { 1 } { 4 } x + 2 = \frac { 6 } { 7 } x - 3$ for x .

A) $\frac { 140 } { 17 }$
B) $\frac { 140 } { 17 }$
C) $\frac { 28 } { 17 }$
D) $\frac { 28 } { 17 }$
E) there is no solution

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