Let's solve the equation [tex]\(\frac{x}{8} = 5\)[/tex] step by step.
1. Understand the equation:
The given equation is [tex]\(\frac{x}{8} = 5\)[/tex].
2. Isolate the variable [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the equation. We can do this by eliminating the denominator (8) from the left side.
3. Eliminate the denominator:
Multiply both sides of the equation by 8 to cancel out the division by 8:
[tex]\[
8 \cdot \frac{x}{8} = 8 \cdot 5
\][/tex]
4. Simplify:
On the left side, the 8 in the numerator and denominator cancel each other out, leaving us with [tex]\(x\)[/tex]. On the right side, multiply [tex]\(8\)[/tex] by [tex]\(5\)[/tex]:
[tex]\[
x = 40
\][/tex]
5. Check the solution:
Substitute [tex]\(x = 40\)[/tex] back into the original equation to verify it satisfies the equation:
[tex]\[
\frac{40}{8} = 5
\][/tex]
Simplifying the left-hand side:
[tex]\[
5 = 5
\][/tex]
Since both sides of the equation are equal, the solution [tex]\(x = 40\)[/tex] is correct.
6. Write the solution in set notation:
The correct choice is:
[tex]\[
\text{A. The solution set is } \{40\}
\][/tex]
Thus, the solution set is [tex]\(\{ 40 \}\)[/tex].
