Sure, let's work through this step-by-step to find the value of [tex]\( y \)[/tex] when [tex]\( x = 10 \)[/tex], given that [tex]\( y \)[/tex] varies inversely as [tex]\( x \)[/tex] and when [tex]\( x = 7 \)[/tex], [tex]\( y = 14 \)[/tex].
### Step-by-Step Solution
1. Understand Inverse Variation Relationship:
- When a variable [tex]\( y \)[/tex] varies inversely as [tex]\( x \)[/tex], the relationship can be expressed as:
[tex]\[
y = \frac{k}{x}
\][/tex]
where [tex]\( k \)[/tex] is a constant.
2. Find the Value of [tex]\( k \)[/tex]:
- We are given that when [tex]\( x = 7 \)[/tex], [tex]\( y = 14 \)[/tex].
- Substitute these values into the equation [tex]\( y = \frac{k}{x} \)[/tex]:
[tex]\[
14 = \frac{k}{7}
\][/tex]
- To solve for [tex]\( k \)[/tex], multiply both sides by 7:
[tex]\[
k = 14 \times 7 = 98
\][/tex]
3. Use the Value of [tex]\( k \)[/tex] to Find [tex]\( y \)[/tex]:
- We need to find [tex]\( y \)[/tex] when [tex]\( x = 10 \)[/tex] using the previously calculated value of [tex]\( k \)[/tex]:
[tex]\[
y = \frac{k}{x} = \frac{98}{10}
\][/tex]
4. Calculate [tex]\( y \)[/tex]:
- Perform the division:
[tex]\[
y = \frac{98}{10} = 9.8
\][/tex]
So, when [tex]\( x = 10 \)[/tex], the value of [tex]\( y \)[/tex] is:
[tex]\[
y = 9.8
\][/tex]
This concludes our solution.
