Question

1. (31) \\(\frac{-4}{0.8} = \frac{2}{x - 1}\\)

Explanation:

Step1: Cross - multiply the proportion

We have the equation \(\frac{-4}{0.8}=\frac{2}{x - 1}\). By the property of proportions (if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)), we get \(- 4\times(x - 1)=0.8\times2\).

Step2: Simplify both sides

First, calculate the right - hand side: \(0.8\times2 = 1.6\). The left - hand side is \(-4x+4\) (using the distributive property \(a(b - c)=ab - ac\) with \(a=-4\), \(b = x\), \(c = 1\)). So the equation becomes \(-4x + 4=1.6\).

Step3: Isolate the variable term

Subtract 4 from both sides of the equation: \(-4x=1.6 - 4\). Calculate \(1.6-4=-2.4\), so \(-4x=-2.4\).

Step4: Solve for x

Divide both sides of the equation by \(-4\): \(x=\frac{-2.4}{-4}\). Calculate \(\frac{-2.4}{-4}=0.6\).

Answer:

\(x = 0.6\)