To solve the given equation [tex]\(\frac{10 - 8x}{3} = -2\)[/tex], we will break down the problem step-by-step. Here is a detailed solution:
[tex]\[
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{Statement} & Reason \\
\hline \(\frac{10-8 x}{3}=-2\) & Given equation \\
\(3\left(\frac{10-8 x}{3}\right)=-2(3)\) & Multiply both sides by 3 to eliminate the denominator \\
\(10-8 x=-6\) & Simplify both sides \\
\(10-8 x-10=-6-10\) & Subtract 10 from both sides to isolate the term with \(x\) \\
\(-8 x=-16\) & Simplify both sides \\
\(\frac{-8 x}{-8}=\frac{-16}{-8}\) & Divide both sides by -8 to solve for \(x\) \\
\(x=2\) & Simplify and get the final result \\
\hline
\end{tabular}
\][/tex]
Explanation of each step:
1. Given equation: Start with the equation provided in the problem.
[tex]\[ \frac{10 - 8x}{3} = -2 \][/tex]
2. Multiply both sides by 3: To eliminate the fraction, we multiply both sides by 3.
[tex]\[ 3 \left( \frac{10 - 8x}{3} \right) = -2 \cdot 3 \][/tex]
This simplifies to:
[tex]\[ 10 - 8x = -6 \][/tex]
3. Subtract 10 from both sides: Our goal is to isolate the term with [tex]\(x\)[/tex], so we subtract 10 from both sides.
[tex]\[ 10 - 8x - 10 = -6 - 10 \][/tex]
This simplifies to:
[tex]\[ -8x = -16 \][/tex]
4. Divide both sides by -8: To solve for [tex]\(x\)[/tex], we divide both sides of the equation by -8.
[tex]\[ \frac{-8x}{-8} = \frac{-16}{-8} \][/tex]
This simplifies to:
[tex]\[ x = 2 \][/tex]
Therefore, the solution to the equation is [tex]\(x = 2\)[/tex].
