Algebra does use numbers. I learned to move the numbers to one side and the variables to the other.
10x+7 = -2x+31
Move 7 to the other side (picking up a minus sign)
10x = -2x + 31 - 7 = -2x + 24
Move -2x to the other side (flipping sign)
12x = 24
Recover 12*2 = 24 via memorization, quick division (though not long division), or whatever method
Therefore, x = 2. Then I drew a square and was done.