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If TU = 7x, UV = x + 5, and TV = 12x + 1, what is TV? 7x T x + 5 U V 12x + 1 Simplify your answer and write it as a proper fraction, mixed number, or integer.

User Jiasli
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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.

User Phoenix Bird
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