Solve the equation 8 ( 6 − x ) − 3 x ( 6 − x ) = 0 8 ( 6 - x ) - 3 x ( 6 - x ) = 0 8 ( 6 − x ) − 3 x ( 6 − x ) = 0 by factoring.A) 8 3 , 6 \frac { 8 } { 3 } , 6 3 8 , 6 B) − 8 3 , − 6 - \frac { 8 } { 3 } , - 6 − 3 8 , − 6 C) 8 3 , 48 \frac { 8 } { 3 } , 48 3 8 , 48 D) 3 8 , 6 \frac { 3 } { 8 } , 6 8 3 , 6 E) − 3 8 , − 48 - \frac { 3 } { 8 } , - 48 − 8 3 , − 48

Question

Solve the equation   8 ( 6 − x )  − 3 x ( 6 − x )  = 0 8 ( 6 - x )  - 3 x ( 6 - x )  = 0 8 ( 6 − x )  − 3 x ( 6 − x )  = 0   by factoring.A)    8 3 , 6 \frac { 8 } { 3 } , 6 3 8 ​ , 6 B)    − 8 3 , − 6 - \frac { 8 } { 3 } , - 6 − 3 8 ​ , − 6 C)    8 3 , 48 \frac { 8 } { 3 } , 48 3 8 ​ , 48 D)    3 8 , 6 \frac { 3 } { 8 } , 6 8 3 ​ , 6 E)    − 3 8 , − 48 - \frac { 3 } { 8 } , - 48 − 8 3 ​ , − 48

Javeria Malick · Accepted Answer

Final Answer : A, Explanation :   First, distribute the terms:   48 − 8 x − 18 x + 3 x 2 = 0 48 - 8x - 18x + 3x^2 = 0 48 − 8 x − 18 x + 3 x 2 = 0  , which simplifies to   3 x 2 − 26 x + 48 = 0 3x^2 - 26x + 48 = 0 3 x 2 − 26 x + 48 = 0  . Factoring this quadratic equation, we get   3 x 2 − 18 x − 8 x + 48 = 0 3x^2 - 18x - 8x + 48 = 0 3 x 2 − 18 x − 8 x + 48 = 0  , which can be grouped and factored further into   3 x ( x − 6 ) − 8 ( x − 6 ) = 0 3x(x - 6) - 8(x - 6) = 0 3 x ( x − 6 ) − 8 ( x − 6 ) = 0  . This gives us   ( 3 x − 8 ) ( x − 6 ) = 0 (3x - 8)(x - 6) = 0 ( 3 x − 8 ) ( x − 6 ) = 0  , leading to the solutions   x = 8 3 x = \frac{8}{3} x = 3 8 ​   and   x = 6 x = 6 x = 6  .

Solve the equation $8 (6 - x) - 3 x (6 - x) = 0$ by factoring.

A) $83,6\frac { 8 } { 3 } , 6$
B) $\frac { 8 } { 3 } , - 6$
C) $83,48\frac { 8 } { 3 } , 48$
D) $38,6\frac { 3 } { 8 } , 6$
E) $\frac { 3 } { 8 } , - 48$

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