Question

1. solve for $overline{de}$

Explanation:

Step1: Set up equation

Since $DF = DE+EF$, we have $(29 + 2x)+8=x + 27$.

Step2: Simplify left - hand side

$29+8 + 2x=x + 27$, so $37+2x=x + 27$.

Step3: Isolate x terms

Subtract $x$ from both sides: $37+2x-x=x + 27-x$, getting $37+x=27$.

Step4: Solve for x

Subtract 37 from both sides: $x=27 - 37=-10$.

Step5: Find DE

Substitute $x = - 10$ into the expression for $DE$ which is $29+2x$. So $DE=29+2\times(-10)=29 - 20 = 11$.

Answer:

$11$