Question

1. -3.8x - 5.9x = 223.1
2. -\frac{3}{5}x - \frac{7}{10}x + \frac{1}{2}x = -56

Explanation:

Step1: Combine like - terms

For the equation \(-3.8x - 5.9x=223.1\), combine the \(x\) terms on the left - hand side. \((-3.8 - 5.9)x=-9.7x\), so the equation becomes \(-9.7x = 223.1\).

Step2: Solve for \(x\)

Divide both sides of the equation \(-9.7x = 223.1\) by \(-9.7\). \(x=\frac{223.1}{-9.7}=-23\).

For the equation \(-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x=-56\), first find a common denominator for the coefficients of \(x\). The common denominator of 5, 10, and 2 is 10.

Step3: Rewrite the coefficients

\(-\frac{3}{5}x=-\frac{6}{10}x\), \(\frac{1}{2}x=\frac{5}{10}x\). The equation becomes \(-\frac{6}{10}x-\frac{7}{10}x+\frac{5}{10}x=-56\).

Step4: Combine like - terms

\((-\frac{6}{10}-\frac{7}{10}+\frac{5}{10})x=-\frac{6 + 7-5}{10}x=-\frac{8}{10}x=-\frac{4}{5}x\). So the equation is \(-\frac{4}{5}x=-56\).

Step5: Solve for \(x\)

Multiply both sides of the equation \(-\frac{4}{5}x=-56\) by \(-\frac{5}{4}\). \(x=-56\times(-\frac{5}{4}) = 70\).

Answer:

For \(-3.8x - 5.9x = 223.1\), \(x=-23\); for \(-\frac{3}{5}x-\frac{7}{10}x+\frac{1}{2}x=-56\), \(x = 70\)