Question

mid-term assessment
solve the equation below
9(m + 5) - 3(m - 2) = 8m + 31
m =

Explanation:

Step1: Expand the brackets

Using the distributive property \(a(b + c)=ab+ac\), we expand \(9(m + 5)\) to \(9m+45\) and \(-3(m - 2)\) to \(-3m + 6\). So the equation becomes:
\(9m+45-3m + 6=8m+31\)

Step2: Combine like terms

Combine the \(m\) terms on the left: \(9m-3m = 6m\), and the constant terms: \(45 + 6=51\). Now the equation is:
\(6m+51=8m+31\)

Step3: Move variable terms to one side

Subtract \(6m\) from both sides:
\(6m - 6m+51=8m-6m + 31\)
Which simplifies to:
\(51 = 2m+31\)

Step4: Move constant terms to the other side

Subtract \(31\) from both sides:
\(51-31=2m+31 - 31\)
\(20 = 2m\)

Step5: Solve for m

Divide both sides by \(2\):
\(\frac{20}{2}=\frac{2m}{2}\)
\(m = 10\)

Answer:

\(10\)