Question

3. What is the solution to this equation? m/4 - 3 = 6 + m/2

Answer 1

Answer:

m = -36

Step-by-step explanation:

Solve for m:

m/4 - 3 = m/2 + 6

Hint: | Put the fractions in m/4 - 3 over a common denominator.

Put each term in m/4 - 3 over the common denominator 4: m/4 - 3 = m/4 - 12/4:

m/4 - 12/4 = m/2 + 6

Hint: | Combine m/4 - 12/4 into a single fraction.

m/4 - 12/4 = (m - 12)/4:

(m - 12)/4 = m/2 + 6

Hint: | Put the fractions in m/2 + 6 over a common denominator.

Put each term in m/2 + 6 over the common denominator 2: m/2 + 6 = m/2 + 12/2:

(m - 12)/4 = m/2 + 12/2

Hint: | Combine m/2 + 12/2 into a single fraction.

m/2 + 12/2 = (m + 12)/2:

(m - 12)/4 = (m + 12)/2

Hint: | Make (m - 12)/4 = (m + 12)/2 simpler by multiplying both sides by a constant.

Multiply both sides by 4:

(4 (m - 12))/4 = (4 (m + 12))/2

Hint: | Cancel common terms in the numerator and denominator of (4 (m - 12))/4.

(4 (m - 12))/4 = 4/4×(m - 12) = m - 12:

m - 12 = (4 (m + 12))/2

Hint: | In (4 (m + 12))/2, divide 4 in the numerator by 2 in the denominator.

4/2 = (2×2)/2 = 2:

m - 12 = 2 (m + 12)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

m - 12 = 2 m + 24

Hint: | Move terms with m to the left hand side.

Subtract 2 m from both sides:

(m - 2 m) - 12 = (2 m - 2 m) + 24

Hint: | Combine like terms in m - 2 m.

m - 2 m = -m:

-m - 12 = (2 m - 2 m) + 24

Hint: | Look for the difference of two identical terms.

2 m - 2 m = 0:

-m - 12 = 24

Hint: | Isolate terms with m to the left hand side.

Add 12 to both sides:

(12 - 12) - m = 12 + 24

Hint: | Look for the difference of two identical terms.

12 - 12 = 0:

-m = 24 + 12

Hint: | Evaluate 24 + 12.

24 + 12 = 36:

-m = 36

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides of -m = 36 by -1:

(-m)/(-1) = -36

Hint: | Any nonzero number divided by itself is one.

(-1)/(-1) = 1:

Answer: m = -36