Algebra Question

Question

Explain how to solve -8=1/4(m-n) for the variable m

Show all steps in the process of solving.

Answer 1

Not sure if you mean -8 = 1/4 (m-n) OR -8 = 1/(4(m-n)), so here are the solutions for both scenarios.

-8 = 1/4 (m-n) (where 4 is the denominator)

Step 1: Multiply both sides by 4:

-32 = 4*(1/4)*(m-n) (4 and 1/4 are reciprocals, so when multiplied together, you get 1)

-32 = 1*(m-n) (1*(m-n) equates to m-n, since 1 is the multiplicative identity element)

-32 = m-n

Step 2: Add n to both sides, in order to isolate m:

-32 + n = m - n + n (-n and n are additive inverses, so their sum is 0)

-32 + n = m + 0 (m + 0 equates to m, since 0 is the additive identity element)

-32 + n = m (-32 + n can also be written as n - 32)

m = n - 32 (Answer)

-8 = 1/(4(m-n)) (where 4(m-n) is the denominator)

Step 1: Take the reciprocal of both sides:

-1/8 = 4(m - n)

Step 2: Divide both sides by 4 (or multiply both sides by 1/4):

(-1/8)(1/4) = 4*(1/4)*(m - n) (4 and 1/4 are reciprocals, so when multiplied together, you get 1)

-1/32 = 1*(m - n) (1*(m-n) equates to m-n, since 1 is the multiplicative identity element)

-1/32 = m - n

Step 3: Add n to both sides, in order to isolate m:

-1/32 + n = m - n + n (-n and n are additive inverses, so their sum is 0)

-1/32 + n = m + 0 (m + 0 equates to m, since 0 is the additive identity element)

-1/32 + n = m (-1/32 + n can also be written as n - 1/32)

m = n - 1/32 (Answer)

Answer 2

You're notation is unclear is it -8=1/4*(m-n) or -8=1/(4*(m-n)