Question

find ml
n 110 + 4x m x + 103 l 70 k
x + 243
find ge
h 13x - 993 g 4 e
3x - 129
3x - 185

Explanation:

Step1: Set up equation for first line segment

Since $NL = NK$, we have $(110 + 4x)+(x + 103)+70=x + 243$.
Simplify the left - hand side: $110+4x+x + 103+70=110+103+70+(4x+x)=283 + 5x$.
So the equation becomes $283+5x=x + 243$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $283+5x−x=x + 243−x$, which gives $283 + 4x=243$.
Subtract 283 from both sides: $4x=243 - 283=-40$.
Divide both sides by 4: $x=\frac{-40}{4}=-10$.

Step3: Find $ML$

Substitute $x = - 10$ into the expression for $ML$ which is $x + 103$.
$ML=-10 + 103=93$.

Step4: Set up equation for second line segment

Since $HF=HE$, we have $13x-993 + 4=3x-129+3x - 185$.
Simplify the right - hand side: $3x-129+3x - 185=6x-314$.
The left - hand side is $13x-989$.
So the equation is $13x-989=6x-314$.

Step5: Solve the new equation for $x$

Subtract $6x$ from both sides: $13x-6x-989=6x-6x-314$, which gives $7x-989=-314$.
Add 989 to both sides: $7x=-314 + 989 = 675$.
Divide both sides by 7: $x=\frac{675}{7}$.

Step6: Find $GE$

$GE=3x-185 + 4=3x-181$.
Substitute $x=\frac{675}{7}$ into the expression for $GE$:
$GE=3\times\frac{675}{7}-181=\frac{2025}{7}-\frac{1267}{7}=\frac{2025 - 1267}{7}=\frac{758}{7}\approx108.29$.

Answer:

$ML = 93$, $GE=\frac{758}{7}$