Let's solve the equation [tex]\(2r - 15 = -9r + 18\)[/tex] step by step.
1. Combine like terms by moving all terms involving [tex]\(r\)[/tex] to one side of the equation and constants to the other side. To do this, add [tex]\(9r\)[/tex] to both sides and add [tex]\(15\)[/tex] to both sides:
[tex]\[
2r + 9r - 15 + 15 = -9r + 9r + 18 + 15
\][/tex]
2. Simplify the equation:
[tex]\[
11r = 33
\][/tex]
3. Solve for [tex]\(r\)[/tex] by dividing both sides of the equation by 11:
[tex]\[
r = \frac{33}{11}
\][/tex]
4. Simplify the fraction:
[tex]\[
r = 3
\][/tex]
Now we need to check if this value of [tex]\(r\)[/tex] is in the given list of possible values: [tex]\(0.3\)[/tex], [tex]\(3\)[/tex], [tex]\(-3\)[/tex], [tex]\(-0.3\)[/tex].
Among the given possibilities, we have [tex]\(r = 3\)[/tex].
Conclusion: The valid solution to the equation [tex]\(2r - 15 = -9r + 18\)[/tex] among the given options is [tex]\(r = 3\)[/tex].
