Question

Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?

-15m = -4m
-7m - 8 = m - 4
-3m - 8 = 4 - m
m - 4 = -7m - 8
-8 - 7m = -4 + m
-8 - 3m = 4 - m

Answer 1

B) -7m - 8 = m - 4

D) m - 4 = -7m - 8

E) -8 - 7m = -4 + m

Explanation:

Solve all of the equations to see if they end up with the same result. Start with the original:

-2m - 5m - 8 = 3 + (-7) + m

-7m - 8 = -4 + m (now we know B and D and E are correct)

-7m - m - 8 = -4 + m - m

-8m - 8 = -4

-8m - 8 + 8= -4 + 8

-8m = 4

Answer 2

-7m - 8 = m - 4

m - 4 = -7m - 8

-8 - 7m = -4 + m

Explanation:

Given equation,

-2m - 5m - 8 = 3 + (-7) + m,

Combining like terms,

-7m - 8 =-4 + m

Subtract m from both sides,

-8m - 8 = -4

Add 8 on both sides,

-8m = 4

Divide both sides by -8,

m =
`-(1)/(2)`

(i) -15m = -4m ⇒ -15m + 4m = 0 ⇒ -11m = 0 ⇒ m = 0

(ii) -7m - 8 = m - 4 ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m =
`-(1)/(2)`

(iii) -3m - 8 = 4 - m ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

(iv) m - 4 = -7m - 8 ⇒ m + 7m = -8 + 4 ⇒ 8m = -4 ⇒ m =
`-(1)/(2)`

(v) -8 - 7m = -4 + m ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m =
`-(1)/(2)`

(vi) -8 - 3m = 4 - m ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6