solving equations with variables on both sides

[dat_atx_chick]

I'm having trouble with solving equations with variables on both sides. For example, how would I solve the following?

. . .-7 + 4m = 6m - 7

I'm also having trouble with the problems that ask if an equation has one unique solution, or if it is an identity, or if it has no solution.

 

[stapel]

To solve an equation with variable terms on both sides, use the addition/subtraction techniques you've learned to get all the variable terms on one side, with the constant terms on the other side. Then solve as usual. For instance:

. . . . .3x + 4 = 5 - x

. . . . .3x + 4 + x = 5 - x + x

. . . . .4x + 4 = 5

. . . . .4x + 4 - 4 = 5 - 4

. . . . .4x = 1

. . . . .(4x)/4 = 1/4

. . . . .x = 1/4

To determine what sort of solution you have, just look at the solution. If it's something like "x = 1/4", then there is just the one solution, namely "x = 1/4". If the solution is something like "0 = 0" or "x = x", then anything will work. If the solution is something like "2 = 4", then clearly nothing will work. So just look at the solution, and apply the definitions.

Eliz.