Question

use the diagram below to answer the prompts.
(note: for the quiz correction, you must answer the alternative question.)
answer
x=
hg=
hf=
ge=

Explanation:

Step1: Set up the equation for \(HF\)

Since \(HF=(13x - 993)+4\) and also \(HF = 3x-129\), we have the equation \(13x-993 + 4=3x-129\).
Simplify the left - hand side: \(13x-989 = 3x-129\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(13x-3x-989=3x - 3x-129\), which gives \(10x-989=-129\).
Add \(989\) to both sides: \(10x-989 + 989=-129+989\), so \(10x = 860\).
Divide both sides by \(10\): \(x=\frac{860}{10}=86\).

Step3: Calculate \(HG\)

Substitute \(x = 86\) into \(HG=13x-993\). Then \(HG=13\times86-993\).
First, calculate \(13\times86=(10 + 3)\times86=10\times86+3\times86=860+258 = 1118\).
Then \(HG=1118-993=125\).

Step4: Calculate \(HF\)

Substitute \(x = 86\) into \(HF=3x-129\). So \(HF=3\times86-129\).
Calculate \(3\times86 = 258\), then \(HF=258-129 = 129\).

Step5: Calculate \(GE\)

Substitute \(x = 86\) into \(GE=3x-185\). Then \(GE=3\times86-185\).
Calculate \(3\times86=258\), then \(GE=258-185 = 73\).

Answer:

\(x = 86\)
\(HG=125\)
\(HF=129\)
\(GE=73\)