To solve the equation [tex]\(3(2t + 5) = 5t + 25\)[/tex], follow these steps:
1. Distribute the 3 on the left-hand side:
[tex]\[
3 \cdot 2t + 3 \cdot 5 = 6t + 15
\][/tex]
So the equation becomes:
[tex]\[
6t + 15 = 5t + 25
\][/tex]
2. Subtract [tex]\(5t\)[/tex] from both sides to move all the terms involving [tex]\(t\)[/tex] to one side:
[tex]\[
6t + 15 - 5t = 5t + 25 - 5t
\][/tex]
Simplifying, we get:
[tex]\[
t + 15 = 25
\][/tex]
3. Subtract 15 from both sides to isolate [tex]\(t\)[/tex]:
[tex]\[
t + 15 - 15 = 25 - 15
\][/tex]
Simplifying this, we find:
[tex]\[
t = 10
\][/tex]
So, the value of [tex]\(t\)[/tex] is [tex]\(10\)[/tex].
Given the choices, [tex]\(5\)[/tex], [tex]\(6\)[/tex], and [tex]\(10\)[/tex], the correct value of [tex]\(t\)[/tex] that satisfies the equation is [tex]\(10\)[/tex].
