To solve the equation [tex]\(9(u-2) + 1.5u = 8.25\)[/tex] and find the value of [tex]\(u\)[/tex], follow these steps:
1. Distribute the 9 through the expression [tex]\( (u-2) \)[/tex]:
[tex]\[
9(u-2) = 9u - 18
\][/tex]
2. Rewrite the original equation using the distributed form:
[tex]\[
9u - 18 + 1.5u = 8.25
\][/tex]
3. Combine like terms on the left-hand side:
[tex]\[
9u + 1.5u - 18 = 8.25
\][/tex]
[tex]\[
10.5u - 18 = 8.25
\][/tex]
4. Isolate the variable term by adding 18 to both sides of the equation:
[tex]\[
10.5u - 18 + 18 = 8.25 + 18
\][/tex]
[tex]\[
10.5u = 26.25
\][/tex]
5. Solve for [tex]\(u\)[/tex] by dividing both sides of the equation by 10.5:
[tex]\[
u = \frac{26.25}{10.5}
\][/tex]
[tex]\[
u = 2.5
\][/tex]
After performing these steps, the value of [tex]\(u\)[/tex] is found to be [tex]\(2.5\)[/tex].
Thus, the solution to the equation [tex]\(9(u-2) + 1.5u = 8.25\)[/tex] is:
[tex]\[
u = 2.5
\][/tex]
