Question

1. 4(4m + 2) - 8 = 30 + m

Explanation:

Step1: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), for \(4(4m + 2)\), we have \(4\times4m+4\times2 = 16m+8\). Then the original equation \(4(4m + 2)-8 = 30 + m\) becomes \(16m+8 - 8=30 + m\).

Step2: Simplify both sides

Simplify the left - hand side: \(16m+(8 - 8)=16m\), so the equation is \(16m=30 + m\).

Step3: Isolate the variable \(m\)

Subtract \(m\) from both sides of the equation: \(16m-m=30 + m - m\). This gives \(15m = 30\).

Step4: Solve for \(m\)

Divide both sides of the equation by 15: \(\frac{15m}{15}=\frac{30}{15}\), so \(m = 2\).

Answer:

\(m = 2\)