Solve for X ,Y, or Z

Question

With a problem like 3x+4=5x-6, how do I know which side to multiply, add, divide, or subtract? When should I combine like terms? How does one distinguish the above problem from 0.3y+2= 0.5y- 3 and what makes them different and why?

Answer 1

3x+4 = 5x-6

add -3x+6 to both sides

10=2x

x = 10/2 = 5

you want to isolate the variable x

one way to think of the solution method is move a number from one side of the equality to the other and change its sign

3x+4 =5x-6 becomes

4+6 = 5x-3x when you move 3x to the right side and -6 to the left side, but change the sign as you do that

then

10=2x

2x =10

x = 10/2 = 5

x=5

.3y+2 = .5y-3 is solved the same way

.5y-.3y = 2+3

.2y = 5

y = 5/.2 = 25

y =25

check the answer

.3(25)+2 = .5(25)-3

7.5+2 = 12.5-3

9.5 = 9.5

no real difference in the two problems

except for keeping track of the decimal places