I just like to add it a diffrent way even though but Emerald wonder is spot on correct.
your given the equation
\(5x - 17 = -x + 7\)
first we gather LIKE TERMS, and when looking at the problem we see that we have 5x and -x on the other side of the equation so now you must gather those two x varibles to the rigth side of the equation so we can solve for x, and even though the x were carrying over is negative it becomes positive because when we carry numbers to another side of an equation we change them to there inverse or recipical wether its a fraction or not.
\(6x - 17 = 7\)
now what we have to do is to make 6x = to the value on the other side of the equation and we can do this by carrying -17 over (In Algebra we pair the sign that is to the left of a number a rule I like to think of it as is that there is no subtraction in algebra only adding of sign's so a good rule to use is that and can be applied to regular mathmatic's as welll not just algebra. after we carry the negative 17 over it becomes a positive 17 and adding that to 7 is 24
\(6x = 24\)
Now are current problems state's 6 time's x is equal to 24 all we have to do is divide 24 by the coefficient of x which is 6 and 24 divided by 6 give's us the quotinet of 4 so this must mean
\(x = 4\)
we can check this by pluging this back into the original equation
\(5(4) - 17 = -(4) + 7\) so lets check this 5*4 - 17 = 3 and -4 + 7 = 3
THE SOLUTION IS CORRECT! x is equal to 4
+444 