Question

1. solve each equation: \\(\frac{1}{x + 4} = 5\\)

Explanation:

Step1: Cross - multiply to eliminate the fraction

Given the equation \(\frac{1}{x + 4}=5\), we can cross - multiply. Multiply both sides of the equation by \(x + 4\) (assuming \(x
eq - 4\) to avoid division by zero). So we get \(1=5\times(x + 4)\).

Step2: Expand the right - hand side

Expand \(5\times(x + 4)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 5\), \(b=x\) and \(c = 4\), so \(5\times(x + 4)=5x+20\). The equation becomes \(1 = 5x+20\).

Step3: Solve for \(x\)

Subtract 20 from both sides of the equation: \(1-20=5x+20 - 20\). This simplifies to \(-19 = 5x\). Then divide both sides by 5: \(x=\frac{-19}{5}=-3.8\). We should also check if this solution makes the original denominator non - zero. When \(x=-3.8\), \(x + 4=-3.8 + 4 = 0.2
eq0\), so the solution is valid.

Answer:

\(x =-\frac{19}{5}\) (or \(x=-3.8\))