# Solving algebraic equations

$10.5x = 5.7x + 29.64$

I've never done anything like the above with two variables of the same on both side, I'm thinking of subtracting 29.64 on the other side but I don't know if I can add it to 10.5x

Hint: Remember that you can do anything to either side of the equation so long as you do the same thing to both sides (so it preserves equality). So try subtracting $5.7x$ from both sides. You'll get:
$$10.5x - 5.7x = 5.7x - 5.7x + 29.64$$ $$4.8x = 0x + 29.64$$
$$4.8x = 29.64$$
How can you get $x$ by itself at this point?
$$10.5x - 5.7x = 5.7x - 5.7x + 29.64$$ $$4.8x = 0x + 29.64$$ $$x = 29.64/4.8$$ $$x = 6.175$$