Solve the equation. x 2 6 − 8 x 7 = − 6 7 \frac { x ^ { 2 } } { 6 } - \frac { 8 x } { 7 } = - \frac { 6 } { 7 } 6 x 2 − 7 8 x = − 7 6 A) x = 7 ; x = − 7 6 x = 7 ; x = - \frac { 7 } { 6 } x = 7 ; x = − 6 7 B) x = − 7 ; x = − 6 7 x = - 7 ; x = - \frac { 6 } { 7 } x = − 7 ; x = − 7 6 C) x = − 6 ; x = − 6 7 x = - 6 ; x = - \frac { 6 } { 7 } x = − 6 ; x = − 7 6 D) x = 6 ; x = 6 7 x = 6 ; x = \frac { 6 } { 7 } x = 6 ; x = 7 6 E) x = − 6 ; x = 7 6 x = - 6 ; x = \frac { 7 } { 6 } x = − 6 ; x = 6 7

Question

Solve the equation.   x 2 6 − 8 x 7 = − 6 7 \frac { x ^ { 2 } } { 6 } - \frac { 8 x } { 7 } = - \frac { 6 } { 7 } 6 x 2 ​ − 7 8 x ​ = − 7 6 ​ A)    x = 7 ; x = − 7 6 x = 7 ; x = - \frac { 7 } { 6 } x = 7 ; x = − 6 7 ​ B)    x = − 7 ; x = − 6 7 x = - 7 ; x = - \frac { 6 } { 7 } x = − 7 ; x = − 7 6 ​ C)    x = − 6 ; x = − 6 7 x = - 6 ; x = - \frac { 6 } { 7 } x = − 6 ; x = − 7 6 ​ D)    x = 6 ; x = 6 7 x = 6 ; x = \frac { 6 } { 7 } x = 6 ; x = 7 6 ​ E)    x = − 6 ; x = 7 6 x = - 6 ; x = \frac { 7 } { 6 } x = − 6 ; x = 6 7 ​

Fanny Marin Marin · Accepted Answer

Final Answer : D, Explanation :   First, we need to multiply both sides of the equation by the common denominator, which is 42. This gives us: 7 x 2 − 48 x = − 36 7x^2 - 48x = -36 7 x 2 − 48 x = − 36 Next, we bring all the terms to one side: 7 x 2 − 48 x + 36 = 0 7x^2 - 48x + 36 = 0 7 x 2 − 48 x + 36 = 0 Finally, we can solve for x using the quadratic formula: x = − ( − 48 ) ± ( − 48 ) 2 − 4 ( 7 ) ( 36 ) 2 ( 7 ) x = \frac{-(-48) \pm \sqrt{(-48)^2 - 4(7)(36)}}{2(7)} x = 2 ( 7 ) − ( − 48 ) ± ( − 48 ) 2 − 4 ( 7 ) ( 36 ) ​ ​ Simplifying: x = 48 ± 2304 − 1008 14 x = \frac{48 \pm \sqrt{2304 - 1008}}{14} x = 14 48 ± 2304 − 1008 ​ ​ x = 48 ± 36 14 x = \frac{48 \pm 36}{14} x = 14 48 ± 36 ​ Which gives us: x = 6 7  or  x = 6 x = \frac{6}{7} 	ext{ or } x= 6 x = 7 6 ​  or  x = 6 Therefore, the answer is D as it includes both solutions.

Solve the equation. $x26−8x7=−67\frac { x ^ { 2 } } { 6 } - \frac { 8 x } { 7 } = - \frac { 6 } { 7 }$

A) $\frac { 7 } { 6 }$
B) $\frac { 6 } { 7 }$
C) $\frac { 6 } { 7 }$
D) $\frac { 6 } { 7 }$
E) $\frac { 7 } { 6 }$

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