Final answer:
To find the value of TV, we set up an equation by adding TU and UV's expressions equal to TV's expression, simplified it, solved for x, and substituted x back into the original equation for TV to reveal that TV equals 13, an integer.
Step-by-step explanation:
The problem involves finding the value of TV when given TU = 7x, UV = x + 5, and TV = 12x + 1. Since TV is the sum of TU and UV, we can set up an equation by adding TU and UV's expressions and set them equal to TV's expression: 7x + (x + 5) = 12x + 1. Next, we simplify the equation and solve for x:
- 7x + x + 5 = 12x + 1
- 8x + 5 = 12x + 1
- 5 - 1 = 12x - 8x
- 4 = 4x
- x = 1
Since we now know x is 1, we substitute it back into the original equation for TV to find its value:
- TV = 12x + 1
- TV = 12(1) + 1
- TV = 12 + 1
- TV = 13
Therefore, the value of TV is 13, which is an integer.