Certainly! Let's solve the given equation step-by-step:
The given function is:
[tex]\[ f(x) = \frac{6}{x} - \frac{6}{2x} \][/tex]
We need to set this function equal to 5:
[tex]\[ \frac{6}{x} - \frac{6}{2x} = 5 \][/tex]
First, let's combine the fractions on the left-hand side by finding a common denominator. The common denominator for [tex]\(x\)[/tex] and [tex]\(2x\)[/tex] is [tex]\(2x\)[/tex]:
[tex]\[ \frac{6}{x} - \frac{6}{2x} = \frac{12}{2x} - \frac{6}{2x} \][/tex]
Now, we can combine the terms:
[tex]\[ \frac{12 - 6}{2x} = \frac{6}{2x} = \frac{3}{x} \][/tex]
So the equation simplifies to:
[tex]\[ \frac{3}{x} = 5 \][/tex]
To solve for [tex]\(x\)[/tex], we clear the fraction by multiplying both sides of the equation by [tex]\(x\)[/tex]:
[tex]\[ 3 = 5x \][/tex]
Next, we isolate [tex]\(x\)[/tex] by dividing both sides by 5:
[tex]\[ x = \frac{3}{5} \][/tex]
Hence, the solution for [tex]\(x\)[/tex] is:
[tex]\[ x = 0.6 \][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\frac{6}{x} - \frac{6}{2x} = 5\)[/tex] is [tex]\(0.6\)[/tex].
