Certainly! Let's solve the given equation [tex]\(x - 5 = 0.1(x + 5)\)[/tex] step by step.
1. Distribute the 0.1 on the right side of the equation:
[tex]\[
x - 5 = 0.1(x) + 0.1(5)
\][/tex]
[tex]\[
x - 5 = 0.1x + 0.5
\][/tex]
2. Move the terms involving [tex]\(x\)[/tex] to one side and the constant terms to the other side:
- Subtract [tex]\(0.1x\)[/tex] from both sides:
[tex]\[
x - 0.1x - 5 = 0.1x - 0.1x + 0.5
\][/tex]
[tex]\[
0.9x - 5 = 0.5
\][/tex]
3. Move the constant term [tex]\(-5\)[/tex] to the other side by adding 5 to both sides:
[tex]\[
0.9x - 5 + 5 = 0.5 + 5
\][/tex]
[tex]\[
0.9x = 5.5
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 0.9:
[tex]\[
x = \frac{5.5}{0.9}
\][/tex]
5. Calculate the value of [tex]\(x\)[/tex]:
[tex]\[
x \approx 6.111111111111111
\][/tex]
6. Round the solution to the nearest hundredth:
[tex]\[
x \approx 6.11
\][/tex]
Thus, the solution [tex]\(x\)[/tex] to the equation [tex]\(x - 5 = 0.1(x + 5)\)[/tex], rounded to the nearest hundredth, is [tex]\(6.11\)[/tex].
