Answer:
[tex]x=18[/tex]
Step-by-step explanation:
[tex](4x-11)\\(2x+25)[/tex]
According to the Alternate Exterior Angles Theorem, "when two lines are cut by a transversal, the resulting alternate exterior angles are congruent."
This means that the two expressions above are to be set equal to each other because they are representative of two alternate exterior angles, which are congruent:
[tex]4x-11=2x+25[/tex]
Add [tex]11[/tex] to both sides of the equation:
[tex]4x=2x+36[/tex]
Subtract [tex]2x[/tex] from both sides of the equation:
[tex]2x=36[/tex]
Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]2[/tex]:
[tex]x=18[/tex]
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Check your work by substituting [tex]18[/tex] for [tex]x[/tex] in the initial equation:
[tex]4(18)-11=2(18)+25[/tex]
[tex]61=61[/tex]
It's correct!
