Question

1. $4|3x - 6| = 28$
2. $left|\frac{2m + 3}{6}

ight| = 5$

1. $|2v + 3| + 7 = 47$
2. $\frac{0.4}{2w} = \frac{3}{0.75}$
3. $\frac{35}{25} = \frac{15 - 1c}{5}$
4. $\frac{6}{4y + 1} = \frac{9}{9y - 6}$

Explanation:

Let's solve problem 31: \(\frac{0.4}{2w}=\frac{3}{0.75}\)

Step 1: Cross - multiply

Cross - multiplying the proportion \(\frac{a}{b}=\frac{c}{d}\) gives \(a\times d = b\times c\). So for \(\frac{0.4}{2w}=\frac{3}{0.75}\), we have \(0.4\times0.75=2w\times3\)
\(0.3 = 6w\)

Step 2: Solve for \(w\)

Divide both sides of the equation \(0.3 = 6w\) by 6.
\(w=\frac{0.3}{6}\)
\(w = 0.05\)

Answer:

\(w = 0.05\)