Answer :

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]