To find Terrance's age, we need to solve the equation given: [tex]\( t - 3.5 = 22.5 \)[/tex].
Here’s the detailed step-by-step solution:
1. Understand the equation: The equation [tex]\( t - 3.5 = 22.5 \)[/tex] represents Terrance being 3.5 years older than Stephanie, where [tex]\( t \)[/tex] is Terrance's age and 22.5 is Stephanie's age.
2. Isolate the variable [tex]\( t \)[/tex]: To find Terrance's age, we need to isolate [tex]\( t \)[/tex] on one side of the equation.
3. Add 3.5 to both sides: To isolate [tex]\( t \)[/tex], we need to eliminate the [tex]\(-3.5\)[/tex] on the left-hand side. We do this by adding 3.5 to both sides of the equation.
[tex]\[
t - 3.5 + 3.5 = 22.5 + 3.5
\][/tex]
4. Simplify the equation: On the left-hand side, [tex]\(-3.5\)[/tex] and [tex]\(+3.5\)[/tex] cancel each other out, leaving us with:
[tex]\[
t = 22.5 + 3.5
\][/tex]
5. Calculate the result:
[tex]\[
t = 26.0
\][/tex]
Therefore, Terrance is [tex]\( 26.0 \)[/tex] years old.
