The equation [tex]$9(u-2) + 1.5u = 8.25$[/tex] models the total miles Michael traveled one afternoon while sledding, where [tex]u[/tex] equals the number of hours walking up a hill and [tex](u-2)[/tex] equals the number of hours sledding down the hill. What is the value of [tex]u[/tex]?

A. [tex]u = 0.25[/tex]
B. [tex]u = 0.75[/tex]
C. [tex]u = 1.1[/tex]
D. [tex]u = 2.5[/tex]



Answer :

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]