Final answer:
By adding the algebraic expressions for DE and EF and setting the sum equal to DF, we solve the equation to find that the value of x is 11.
Step-by-step explanation:
To find the value of x when DE = 5x - 9, EF = 2x + 10, and DF = 78, we need to understand that DE + EF = DF if DE, EF, and DF are segments of a straight line and DE and EF are adjacent segments.
To find the value of x, we can use the fact that in a line segment, the sum of the length of its two parts is equal to the length of the whole line segment. Using this fact, we can set up the equation: DE + EF = DF. Substituting the given expressions, we have (5x-9) + (2x+10) = 78. Combining like terms and solving for x, we get 7x + 1 = 78. Subtracting 1 from both sides, we have 7x = 77. Dividing both sides by 7, we find x = 11.
Therefore:
- (5x - 9) + (2x + 10) = 78
- 7x + 1 = 78
- 7x = 77
- x = 11
The value of x is 11.