Question

6(m-1) = 3(3m + 2) Show all work

Answer 1

GiveN:

• 6(m - 1) = 3(3m + 2)

What to do?

• We have to solve for m
  `.`

Solution:

The equation has only one variable i.e. m. For finding m we need to isolate it any one side of the equation. Before that, let's expand the parentheses,

⇒ 6(m - 1) = 3(3m + 2)

⇒ 6m - 6 = 9m + 6

Now moving m to the left hand side and constant terms to the right hand side,

⇒ 6m - 9m = 6 + 6

⇒ -3m = 12

Dividing the Equation by -3,

⇒ m = 12 / -3

⇒ m = -4

Thus, the required value of m is -4.

Answer 2

`\boxed{\sf m = -4}`

Explanation:

`\sf Solve \: for \: m: \\ \sf \implies 6 (m - 1) = 3 (3 m + 2) \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \sf \implies 6 m - 6 = 3 (3 m + 2) \\ \\ \sf Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ \sf \implies 6 m - 6 = 9 m + 6 \\ \\ \sf Subtract \: 9 m \: from \: both \: sides: \\ \sf \implies (6 m - 9 m) - 6 = (9 m - 9 m) + 6 \\ \\ \sf 6 m - 9 m = -3 m: \\ \sf \implies -3 m - 6 = (9 m - 9 m) + 6 \\ \\ \sf 9 m - 9 m = 0: \\ \sf \implies -3 m - 6 = 6 \\ \\ \sf Add \: 6 \: to \: both \: sides: \\ \sf \implies (6 - 6) - 3 m = 6 + 6 \\ \\ \sf 6 - 6 = 0: \\ \sf \implies -3 m = 6 + 6 \\ \\ \sf 6 + 6 = 12: \\ \sf \implies -3 m = 12 \\ \\ \sf Divide \: both \: sides \: of \: -3 m = 12 \: by \: -3: \\ \sf \implies ( - 3m)/( - 3) = (12)/( - 3) \\ \\ \sf ( - 3)/( - 3) = 1: \\ \sf \implies m = (12)/( - 3) \\ \\ \sf - (12)/(3) = - 4 : \\ \sf \implies m = - 4`