how do you solve a problem like...
solve with add and multiply 5+6x<53

5 + 6x \lt 53

Add -5 to both sides

5 + 6x -5 \lt 53 - 5

6x \lt 48

Now multiply by 1/6

\frac {6x}{6} \lt \frac {48}{6}

x \, \lt \, 8

If ever you multiply or divide by -1, you need to change the "sense" of the inequality ("<" changes to ">" or ">" to "<", for example). If you ever have to divide or multiply by "x", you need to make sure (at the end) that "x" is positive. Otherwise, the sign changes.