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If DE = 3x+4, EF = 2x+1, and DF = 6x-7, find DF

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Final answer:

To find the length of DF when DE = 3x+4, EF = 2x+1, and DF = 6x-7, we set up the equation (3x+4) + (2x+1) = 6x-7, solve for x, and then substitute x back into the expression for DF. The result is that DF is 65 units long.

Step-by-step explanation:

If we have a situation where DE, EF, and DF represent segments of a line, and the lengths of those segments are given by the expressions DE = 3x+4, EF = 2x+1, and DF = 6x-7, we can find the value of DF by setting up an equation that reflects this relationship. Since DE and EF are consecutive segments on the same line, we know that DE + EF = DF. Substituting in the given expressions, we have (3x+4) + (2x+1) = 6x-7.

Solving for x involves combining like terms and isolating the variable:

  • 3x + 4 + 2x + 1 = 6x - 7
  • 5x + 5 = 6x - 7
  • x = 5 + 7
  • x = 12

Now that we have the value for x, we can find DF by substituting x back into the expression for DF:

  • DF = 6x - 7
  • DF = 6(12) - 7
  • DF = 72 - 7
  • DF = 65

Therefore, the length of segment DF is 65 units.

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