Question

if de = x + 3, ef = 6x, and df = 10, what is de? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation based on line - segment addition

Since $DF=DE + EF$, we have the equation $(x + 3)+6x=10$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $x+6x + 3=10$, which simplifies to $7x+3 = 10$.

Step3: Isolate the variable term

Subtract 3 from both sides of the equation: $7x+3−3=10 - 3$, resulting in $7x=7$.

Step4: Solve for $x$

Divide both sides by 7: $\frac{7x}{7}=\frac{7}{7}$, so $x = 1$.

Step5: Find the value of $DE$

Substitute $x = 1$ into the expression for $DE$. Since $DE=x + 3$, then $DE=1+3=4$.

Answer:

4