IDNLearn.com provides a platform for sharing and gaining valuable knowledge. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.
Sagot :
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].
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].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.