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.