To solve the equation [tex]\(\frac{x}{6} = 8\)[/tex] for the variable [tex]\(x\)[/tex], follow these steps:
1. Understand the equation: The given equation [tex]\(\frac{x}{6} = 8\)[/tex] states that [tex]\(x\)[/tex] divided by 6 equals 8.
2. Isolate the variable [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], we need to eliminate the fraction. This can be done by multiplying both sides of the equation by 6.
The reason we multiply by 6 is to cancel out the denominator on the left-hand side of the equation.
3. Multiply both sides by 6:
[tex]\[
\left(\frac{x}{6}\right) \times 6 = 8 \times 6
\][/tex]
4. Simplify the equation:
On the left-hand side:
[tex]\[
\left(\frac{x}{6}\right) \times 6 = x
\][/tex]
since [tex]\(6\)[/tex] in the numerator and denominator cancels each other out.
Therefore:
[tex]\[
x = 8 \times 6
\][/tex]
5. Calculate the multiplication:
[tex]\[
8 \times 6 = 48
\][/tex]
So, the value of [tex]\(x\)[/tex] is 48.
Therefore, the solution to the equation [tex]\(\frac{x}{6} = 8\)[/tex] is:
[tex]\[
x = 48
\][/tex]
