To solve the equation [tex]\(x - 5 = 0.1(x + 5)\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Distribute the 0.1 on the right-hand side:
[tex]\[
x - 5 = 0.1x + 0.5
\][/tex]
2. Isolate the terms involving [tex]\(x\)[/tex] on one side. Subtract [tex]\(0.1x\)[/tex] from both sides:
[tex]\[
x - 0.1x - 5 = 0.5
\][/tex]
3. Combine like terms:
[tex]\[
0.9x - 5 = 0.5
\][/tex]
4. Add 5 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
0.9x = 5.5
\][/tex]
5. Divide both sides by 0.9 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{5.5}{0.9}
\][/tex]
6. Perform the division:
[tex]\[
x \approx 6.111111111111111
\][/tex]
7. Round the result to the nearest hundredth:
[tex]\[
x \approx 6.11
\][/tex]
Thus, Kelli can swim about [tex]\(6.11 \, \text{km/hr}\)[/tex].
