book Maths Puzzle Numerical Ability

Can you please explain to me what an algebraic proof is? I know you give a statement such as: all alternate interior angles are congruent. But how would you prove the statement?

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Solve each equation.

c/4= 16
1/2x= 48
-6d= -42
19= 3y - 5
6- 5c= -29
0.4s - 3= -1
4x - 9= 7x + 12
-4(2-3x) = 7 - 2(x-3)

these are giving me a headache! How much water should be added to 30 gallons of a solution that is 70% antifreeze in order to get a mixture that is 60% antifreeze?