Is x=3 the solution to the equation 8+3 (x-1) = 5x-1? How do you know

So we have;

8 + 3 (x - 1) = 5x - 1

Opening the brackets we get;

8 + 3x - 3 = 5x - 1

Taking all x terms to the left and all integers to right;

8 - 3 + 1 = 5x - 3x

9 - 3 = 2x

6 = 2x

This can also be arranged as;

2x = 6

x = 6 : 2 = 3

So x = 3

To see if the solution to the equation is 3, you would have to plug 3 into the equation for the x's like this

8 + 3 (3 - 1) = 5 (3) - 1

8 + 9 - 3 = 15 - 1

17 - 3 = 14

14 = 14

3 is the solution to the equation because 14 = 14.