Question

h) \\(\frac{3}{4}(24 + w) = w\\)

Explanation:

Step1: Expand the left - hand side

We use the distributive property \(a(b + c)=ab+ac\). Here \(a = \frac{3}{4}\), \(b = 24\) and \(c = w\). So \(\frac{3}{4}(24 + w)=\frac{3}{4}\times24+\frac{3}{4}w\). Calculating \(\frac{3}{4}\times24\), we get \(18\). So the equation becomes \(18+\frac{3}{4}w=w\).

Step2: Subtract \(\frac{3}{4}w\) from both sides

Subtract \(\frac{3}{4}w\) from both sides of the equation \(18+\frac{3}{4}w = w\). We have \(18+\frac{3}{4}w-\frac{3}{4}w=w - \frac{3}{4}w\). Simplifying both sides, the left - hand side is \(18\) and the right - hand side is \(\frac{1}{4}w\). So the equation is \(18=\frac{1}{4}w\).

Step3: Solve for \(w\)

Multiply both sides of the equation \(18=\frac{1}{4}w\) by \(4\) to isolate \(w\). We get \(18\times4=\frac{1}{4}w\times4\). Calculating \(18\times4 = 72\) and \(\frac{1}{4}w\times4=w\). So \(w = 72\).

Answer:

\(w = 72\)