Sure, let's solve the equation step by step:
We start with the given equation:
[tex]\[ 9(u - 2) + 1.5u = 8.25 \][/tex]
Step 1: Expand the equation.
First, distribute the 9 through the [tex]\((u - 2)\)[/tex]:
[tex]\[ 9u - 18 + 1.5u = 8.25 \][/tex]
Step 2: Combine like terms.
Now, combine the [tex]\(9u\)[/tex] and the [tex]\(1.5u\)[/tex]:
[tex]\[ 10.5u - 18 = 8.25 \][/tex]
Step 3: Isolate the variable term.
To isolate the term with [tex]\(u\)[/tex], we need to add 18 to both sides of the equation:
[tex]\[ 10.5u - 18 + 18 = 8.25 + 18 \][/tex]
[tex]\[ 10.5u = 26.25 \][/tex]
Step 4: Solve for [tex]\(u\)[/tex].
Now, divide both sides of the equation by 10.5:
[tex]\[ u = \frac{26.25}{10.5} \][/tex]
[tex]\[ u = 2.5 \][/tex]
So, the solution to the equation is:
[tex]\[ u = 2.5 \][/tex]
Therefore, the value of [tex]\(u\)[/tex] is:
[tex]\[ \boxed{2.5} \][/tex]
