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Solve for [tex]\( x \)[/tex]:
[tex]\[ 3x = 6x - 2 \][/tex]



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Given the equation [tex]\( 2x - 8 = 4y \)[/tex], complete the following table:

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$ & -8 & -6 & -4 & -2 & 0 \\
\hline
$y$ & & & & & \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
Certainly! Let's solve the equation [tex]\(2x - 8 = 4y\)[/tex] for the given [tex]\(x\)[/tex] values step-by-step. The goal is to find the corresponding [tex]\(y\)[/tex] values.

The equation given is:
[tex]\[2x - 8 = 4y\][/tex]

First, we need to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex]:
[tex]\[2x - 8 = 4y\][/tex]

Step 1: Isolate [tex]\(y\)[/tex] by first subtracting 8 from both sides:
[tex]\[2x - 8 = 4y\][/tex]

Step 2: Divide both sides by 4 to solve for [tex]\(y\)[/tex]:
[tex]\[y = \frac{2x - 8}{4}\][/tex]
[tex]\[y = \frac{2x}{4} - \frac{8}{4}\][/tex]
[tex]\[y = \frac{x}{2} - 2\][/tex]

Now that we have the expression for [tex]\(y\)[/tex]:
[tex]\[y = \frac{x}{2} - 2\][/tex]

We can calculate [tex]\(y\)[/tex] for each given [tex]\(x\)[/tex] value.

### For [tex]\(x = -8\)[/tex]:
[tex]\[y = \frac{-8}{2} - 2\][/tex]
[tex]\[y = -4 - 2\][/tex]
[tex]\[y = -6\][/tex]

### For [tex]\(x = -6\)[/tex]:
[tex]\[y = \frac{-6}{2} - 2\][/tex]
[tex]\[y = -3 - 2\][/tex]
[tex]\[y = -5\][/tex]

### For [tex]\(x = -4\)[/tex]:
[tex]\[y = \frac{-4}{2} - 2\][/tex]
[tex]\[y = -2 - 2\][/tex]
[tex]\[y = -4\][/tex]

### For [tex]\(x = -2\)[/tex]:
[tex]\[y = \frac{-2}{2} - 2\][/tex]
[tex]\[y = -1 - 2\][/tex]
[tex]\[y = -3\][/tex]

### For [tex]\(x = 0\)[/tex]:
[tex]\[y = \frac{0}{2} - 2\][/tex]
[tex]\[y = 0 - 2\][/tex]
[tex]\[y = -2\][/tex]

Now we can complete the table with the calculated [tex]\(y\)[/tex] values:
[tex]\[ \begin{tabular}{|l|l|l|l|l|l|} \hline $x$ & -8 & -6 & -4 & -2 & 0 \\ \hline $y$ & -6 & -5 & -4 & -3 & -2 \\ \hline \end{tabular} \][/tex]

So, the completed table is:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -8 & -6 & -4 & -2 & 0 \\ \hline y & -6 & -5 & -4 & -3 & -2 \\ \hline \end{array} \][/tex]

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