Question

Solve for m.


`(5)/(4 - m) = ( - 3)/(m + 2)`


A.
`- (11)/(3)`

B.
`- 11`

C.
`- (7)/(3)`

D.
`- 3`​

Answer 1

Hello,

`(5)/(4 - m) = ( - 3)/(2 + m)`

`5(2 + m) = - 3(4 - m)`

`10 + 5m = - 12 + 3m`

`5m - 3m = - 12 - 10`

`2m = - 22`

`m = ( - 22)/(2)`

`m = - 11`

→ Answer B

Answer 2

Variable m cannot be equal to any of the values −2,4 as division by zero is undefined. Multiply both sides of the equation by (m − 4)(m + 2), the lowest common denominator of 4−m,m + 2.

• −(2 + m) ×5 = (m −4 )( −3 )

To find the opposite of 2+m, find the opposite of each term.

• (−2 −m) ×5 = ( m−4 )( −3 )

Use the distributive property to multiply −2−m by 5.

• −10 −5m = ( m−4 )( −3 )

Use the distributive property to multiply m−4 by −3.

• −10 −5m =−3m + 12

Add 3m to both sides.

• −10 − 5m + 3m =12

Combine −5m and 3m to get −2m.

• −10 −2m = 12

Add 10 to both sides.

• −2m = 12 + 10

Add 12 and 10 to get 2.

• −2m = 22

Divide both sides by −2.

• m = 22 / -2

Divide 22 by −2 to get −11.

• m = −11

Therefore, the correct option is "B".