The first question's equation is solved correctly, so true.
Q2: -2x+5=4x-7 ...subtract 5 from both sides
-2x=4x-12 ...subtract 4x from both sides
-6x=-12 ...divide both sides by -6
x=2
Q3: 12y+4=8y-12 ...subtract 4 from both sides
12y=8y-16 ...subtract 8y from both sides
4y=-16 ... divide both sides by 4
y=-4
Q4: 7z-18=-2z+18 ...add 18 to both sides
7z=-2z+36 ...add 2z to both sides
9z=36 ...divide both sides by 9
z=4
Q5: 10x+15=5x-10 ...subtract 15 from both sides
10x=5x-25 ...subtract 5x from both sides
5x=-25 ...divide both sides by 5x
x=-5
Hope this helps :-)