Answer:
[tex]x=10[/tex]
Step-by-step explanation:
Supplementary angles are angles equal to 180°.
Therefore:
[tex]4(2x+9)+2(4x-8)=180[/tex]
Now that we have our equation, let's distribute the [tex]4[/tex] and the [tex]2[/tex] into the parentheses they are next to:
[tex]8x+36+8x-16=180[/tex]
Combine like terms:
[tex]16x+20=180[/tex]
Subtract [tex]20[/tex] from both sides of the equation:
[tex]16x=160[/tex]
Divide by the coefficient of [tex]x[/tex], which is [tex]16[/tex]:
[tex]x=10[/tex]
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Check your work by substituting [tex]10[/tex] into one of the equations above:
[tex]8(10)+36+8(10)-16=180[/tex]
[tex]80+36+80-16=180[/tex]
[tex]180=180[/tex]
It's correct!
