Question

1. everything you do to one side, you have to ______.

do to the other side
not do to the other side

1. how are inequalities and equations different?

inequalities have only 1 solution while equations have many
inequalities have many solutions while equations only have 1
inequalities dont have solutions but equations do

Explanation:

Question 1

In solving equations (and inequalities), the principle of balance requires that any operation performed on one side must also be performed on the other side to maintain equality (or the inequality relationship in a consistent way). So the correct option is the one that says you have to do the same to the other side.

Equations typically (for linear equations in one variable) have one solution, while inequalities (like \(x > 3\)) have infinitely many solutions (all numbers greater than 3). The first option reverses this, so the correct one is the second option stating inequalities have many solutions while equations only have 1 (for linear cases, though some equations can have more, but this is the intended concept here).

Answer:

A. do to the other side (assuming the first option is labeled A, the second B; if labels aren't given, the first option "do to the other side")

Question 2