To determine whether each given value of [tex]\( w \)[/tex] is a solution to the equation [tex]\( 18 = 3(w - 2) \)[/tex], we need to substitute each value of [tex]\( w \)[/tex] into the equation and check if it results in a true statement. We'll evaluate this for each value provided: -10, 6, 1, and -2.
1. For [tex]\( w = -10 \)[/tex]:
[tex]\[
18 = 3(-10 - 2)
\][/tex]
Calculate inside the parentheses first:
[tex]\[
-10 - 2 = -12
\][/tex]
Then multiply by 3:
[tex]\[
3(-12) = -36
\][/tex]
The equation becomes:
[tex]\[
18 = -36
\][/tex]
This is not true, so [tex]\( w = -10 \)[/tex] is not a solution.
2. For [tex]\( w = 6 \)[/tex]:
[tex]\[
18 = 3(6 - 2)
\][/tex]
Calculate inside the parentheses first:
[tex]\[
6 - 2 = 4
\][/tex]
Then multiply by 3:
[tex]\[
3(4) = 12
\][/tex]
The equation becomes:
[tex]\[
18 = 12
\][/tex]
This is not true, so [tex]\( w = 6 \)[/tex] is not a solution.
3. For [tex]\( w = 1 \)[/tex]:
[tex]\[
18 = 3(1 - 2)
\][/tex]
Calculate inside the parentheses first:
[tex]\[
1 - 2 = -1
\][/tex]
Then multiply by 3:
[tex]\[
3(-1) = -3
\][/tex]
The equation becomes:
[tex]\[
18 = -3
\][/tex]
This is not true, so [tex]\( w = 1 \)[/tex] is not a solution.
4. For [tex]\( w = -2 \)[/tex]:
[tex]\[
18 = 3(-2 - 2)
\][/tex]
Calculate inside the parentheses first:
[tex]\[
-2 - 2 = -4
\][/tex]
Then multiply by 3:
[tex]\[
3(-4) = -12
\][/tex]
The equation becomes:
[tex]\[
18 = -12
\][/tex]
This is not true, so [tex]\( w = -2 \)[/tex] is not a solution.
Here is the table summarizing the results:
\begin{tabular}{|c|c|c|}
\hline \multirow{2}{*}{[tex]$w$[/tex]} & \multicolumn{2}{|c|}{Is it a solution?} \\
\cline{2-3} & Yes & No \\
\hline
-10 & & [tex]\(\bigcirc\)[/tex] \\
\hline
6 & & [tex]\(\bigcirc\)[/tex] \\
\hline
1 & & [tex]\(\bigcirc\)[/tex] \\
\hline
-2 & & [tex]\(\bigcirc\)[/tex] \\
\hline
\end{tabular}
Thus, none of the given values for [tex]\( w \)[/tex] is a solution to the equation [tex]\( 18 = 3(w - 2) \)[/tex].
