To solve the equation [tex]\( 9(u - 2) + 1.5u = 8.25 \)[/tex] for the variable [tex]\( u \)[/tex], we need to follow these steps:
1. Expand the Equation:
Distribute the constants 9 and 1.5 across their respective terms inside the parentheses.
[tex]\[
9(u - 2) + 1.5u = 8.25
\][/tex]
[tex]\[
9u - 18 + 1.5u = 8.25
\][/tex]
2. Combine Like Terms:
Combine the terms containing [tex]\( u \)[/tex] on the left side of the equation.
[tex]\[
(9u + 1.5u) - 18 = 8.25
\][/tex]
[tex]\[
10.5u - 18 = 8.25
\][/tex]
3. Isolate the Variable:
Add 18 to both sides of the equation to isolate the term with [tex]\( u \)[/tex].
[tex]\[
10.5u - 18 + 18 = 8.25 + 18
\][/tex]
[tex]\[
10.5u = 26.25
\][/tex]
4. Solve for [tex]\( u \)[/tex]:
Divide both sides of the equation by 10.5 to solve for [tex]\( u \)[/tex].
[tex]\[
u = \frac{26.25}{10.5}
\][/tex]
5. Simplify the Fraction:
Simplify the fraction to find the value of [tex]\( u \)[/tex].
[tex]\[
u = 2.5
\][/tex]
Therefore, the value of [tex]\( u \)[/tex] is [tex]\( 2.5 \)[/tex].
Hence, the correct answer is:
[tex]\[ u = 2.5 \][/tex]
