Question

1. -5 - 5(m - 8) = 4m - 19

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b - c)=ab - ac\). Here \(a=-5\), \(b = m\), \(c = 8\). So \(-5-5(m - 8)=-5-5m + 40\).
\(-5-5m + 40=35-5m\)

Step2: Set up the new equation

The original equation \(-5-5(m - 8)=4m - 19\) becomes \(35-5m=4m - 19\).

Step3: Add \(5m\) to both sides

To get all the \(m\) terms on one side. \(35-5m+5m=4m - 19+5m\).
\(35 = 9m-19\)

Step4: Add 19 to both sides

To isolate the term with \(m\). \(35 + 19=9m-19 + 19\).
\(54=9m\)

Step5: Solve for \(m\)

Divide both sides by 9. \(\frac{54}{9}=\frac{9m}{9}\).
\(m = 6\)

Answer:

\(m = 6\)