Ray AP bisects angle ∠CAT, this means that it divides the angle in two equal halves. In other words angles ∠PAT and ∠PAC are equal.
And if you add both angles you'll get the measure of ∠CAT.
∠CAT=∠PAT+∠PAC
and
∠PAT=∠PAC
Then
∠CAT=2*∠PAT
Now if ∠CAT=5x+17 and ∠PAT=3x-4, you can replace these expressions with the equation determined before to make a one unknown equation:
[tex]\begin{gathered} \angle\text{CAT}=2(\angle\text{PAT)} \\ 5x+17=2(3x-4) \end{gathered}[/tex]
From this you can clear the value of x:
First step: solve the terms in parenthesis by applying the distributive properties of multiplication
[tex]\begin{gathered} 5x+17=2(3x-4) \\ 5x+17=2\cdot3x-2\cdot4 \\ 5x+17=6x-8 \end{gathered}[/tex]
Next is to pass all x-related terms to one side of the equation and all related terms to the other side
[tex]\begin{gathered} 5x+17=6x-8 \\ 5x-6x=-8-17 \\ -x=-25 \\ x=25 \end{gathered}[/tex]
