Answer:
The solution of the equation [tex]5x\:+\:1\:=\:9\:+\:3x[/tex] is [tex]\boxed{x=4}[/tex]
So, option A is the correct option.
Step-by-step explanation:
'5 times a number, plus 1, is equal to 9 added to 3 times the number' is algebraically represented as:
[tex]5x\:+\:1\:=\:9\:+\:3x[/tex]
Lets solve the equation to determine the solution
so
[tex]5x\:+\:1\:=\:9\:+\:3x[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]
[tex]5x+1-1=9+3x-1[/tex]
[tex]5x=3x+8[/tex]
[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]
[tex]5x-3x=3x+8-3x[/tex]
[tex]2x=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]\frac{2x}{2}=\frac{8}{2}[/tex]
[tex]x=4[/tex]
Thus, the solution of the equation [tex]5x\:+\:1\:=\:9\:+\:3x[/tex] is [tex]\boxed{x=4}[/tex]
Therefore, from the above calculations, we conclude that option A is the correct option.
