Let's consider the equation [tex]\(\frac{x}{5} - 2 = 11\)[/tex] and verify which one of the given values satisfies this equation.
We are given the potential solutions:
- [tex]\(x = 1.8\)[/tex]
- [tex]\(x = 2.6\)[/tex]
- [tex]\(x = 45\)[/tex]
- [tex]\(x = 65\)[/tex]
We will substitute each value into the equation and check if the equation holds true.
1. Substitute [tex]\(x = 1.8\)[/tex]:
[tex]\[
\frac{1.8}{5} - 2
\][/tex]
Calculate [tex]\(\frac{1.8}{5}\)[/tex]:
[tex]\[
\frac{1.8}{5} = 0.36
\][/tex]
Then:
[tex]\[
0.36 - 2 = -1.64
\][/tex]
Since [tex]\(-1.64 \neq 11\)[/tex], [tex]\(x = 1.8\)[/tex] is not a solution.
2. Substitute [tex]\(x = 2.6\)[/tex]:
[tex]\[
\frac{2.6}{5} - 2
\][/tex]
Calculate [tex]\(\frac{2.6}{5}\)[/tex]:
[tex]\[
\frac{2.6}{5} = 0.52
\][/tex]
Then:
[tex]\[
0.52 - 2 = -1.48
\][/tex]
Since [tex]\(-1.48 \neq 11\)[/tex], [tex]\(x = 2.6\)[/tex] is not a solution.
3. Substitute [tex]\(x = 45\)[/tex]:
[tex]\[
\frac{45}{5} - 2
\][/tex]
Calculate [tex]\(\frac{45}{5}\)[/tex]:
[tex]\[
\frac{45}{5} = 9
\][/tex]
Then:
[tex]\[
9 - 2 = 7
\][/tex]
Since [tex]\(7 \neq 11\)[/tex], [tex]\(x = 45\)[/tex] is not a solution.
4. Substitute [tex]\(x = 65\)[/tex]:
[tex]\[
\frac{65}{5} - 2
\][/tex]
Calculate [tex]\(\frac{65}{5}\)[/tex]:
[tex]\[
\frac{65}{5} = 13
\][/tex]
Then:
[tex]\[
13 - 2 = 11
\][/tex]
Since [tex]\(11 = 11\)[/tex], [tex]\(x = 65\)[/tex] is a solution.
Therefore, the correct solution to the equation [tex]\(\frac{x}{5} - 2 = 11\)[/tex] is [tex]\(x = 65\)[/tex].
