Final answer:
To solve 6(2t-4)=48-6t, we distribute the 6, combine like terms, and isolate t to find the solution set is {4}.
Step-by-step explanation:
To solve the equation 6(2t-4)=48-6t, we need to expand the left side and then collect like terms. First, we distribute the 6 across the parentheses:
6 × 2t - 6 × 4 = 48 - 6t
12t - 24 = 48 - 6t
Now we add 6t to both sides of the equation and add 24 to both sides to isolate the variable t:
12t + 6t = 48 + 24
18t = 72
Finally, we divide both sides by 18 to find the value of t:
18t / 18 = 72 / 18
t = 4
The solution set is {4}. This means that the value of t that satisfies the equation 6(2t-4)=48-6t is 4.