Get personalized and accurate responses to your questions with IDNLearn.com. Discover comprehensive answers from knowledgeable members of our community, covering a wide range of topics to meet all your informational needs.
Sagot :
Certainly! Let's break down the solution step-by-step.
1. List the terms:
The terms given are:
[tex]\[ x,\ x + 3,\ x - 5,\ 2x,\ 3x \][/tex]
2. Calculate the mean of the terms:
To find the mean, sum all the terms and then divide by the number of terms.
First, the sum of the terms:
[tex]\[ x + (x + 3) + (x - 5) + 2x + 3x = x + x + 3 + x - 5 + 2x + 3x \][/tex]
Simplify the sum:
[tex]\[ x + x + x + 2x + 3x + 3 - 5 = 8x - 2 \][/tex]
Now, divide by the number of terms. There are 5 terms:
[tex]\[ \text{Mean} = \frac{8x - 2}{5} \][/tex]
3. Set the mean equal to [tex]$3x$[/tex]:
According to the problem, the mean of these terms is equal to [tex]$3x$[/tex]:
[tex]\[ \frac{8x - 2}{5} = 3x \][/tex]
4. Solve for [tex]$x$[/tex]:
To solve for [tex]$x$[/tex], start by eliminating the fraction by multiplying both sides of the equation by 5:
[tex]\[ 8x - 2 = 15x \][/tex]
Next, isolate [tex]$x$[/tex]. Subtract [tex]$8x$[/tex] from both sides of the equation:
[tex]\[ -2 = 15x - 8x \][/tex]
Simplify:
[tex]\[ -2 = 7x \][/tex]
Finally, divide both sides by 7:
[tex]\[ x = \frac{-2}{7} \][/tex]
Hence, the solution is:
[tex]\[ x = -\frac{2}{7} \][/tex]
1. List the terms:
The terms given are:
[tex]\[ x,\ x + 3,\ x - 5,\ 2x,\ 3x \][/tex]
2. Calculate the mean of the terms:
To find the mean, sum all the terms and then divide by the number of terms.
First, the sum of the terms:
[tex]\[ x + (x + 3) + (x - 5) + 2x + 3x = x + x + 3 + x - 5 + 2x + 3x \][/tex]
Simplify the sum:
[tex]\[ x + x + x + 2x + 3x + 3 - 5 = 8x - 2 \][/tex]
Now, divide by the number of terms. There are 5 terms:
[tex]\[ \text{Mean} = \frac{8x - 2}{5} \][/tex]
3. Set the mean equal to [tex]$3x$[/tex]:
According to the problem, the mean of these terms is equal to [tex]$3x$[/tex]:
[tex]\[ \frac{8x - 2}{5} = 3x \][/tex]
4. Solve for [tex]$x$[/tex]:
To solve for [tex]$x$[/tex], start by eliminating the fraction by multiplying both sides of the equation by 5:
[tex]\[ 8x - 2 = 15x \][/tex]
Next, isolate [tex]$x$[/tex]. Subtract [tex]$8x$[/tex] from both sides of the equation:
[tex]\[ -2 = 15x - 8x \][/tex]
Simplify:
[tex]\[ -2 = 7x \][/tex]
Finally, divide both sides by 7:
[tex]\[ x = \frac{-2}{7} \][/tex]
Hence, the solution is:
[tex]\[ x = -\frac{2}{7} \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.