To solve the inequality "3 less than a number [tex]\( t \)[/tex] is at most 7," let's break it down step-by-step:
1. First, let's translate the given statement into a mathematical inequality:
[tex]\[ t - 3 \leq 7 \][/tex]
2. The goal is to isolate [tex]\( t \)[/tex] on one side of the inequality. To do this, we need to eliminate the -3 from the left-hand side. We can do this by adding 3 to both sides of the inequality.
3. Add 3 to both sides:
[tex]\[ t - 3 + 3 \leq 7 + 3 \][/tex]
4. Simplify both sides:
[tex]\[ t \leq 10 \][/tex]
So, the final inequality is:
[tex]\[ t \leq 10 \][/tex]
This means the value of [tex]\( t \)[/tex] can be any number that is less than or equal to 10.
