A Bracket on the Way

In $2\left(x-3\right) \ge 4$, the bracket is multiplied by 2. When the other side divides by 2 with no remainder, the quickest first step is to divide both sides by 2. The bracket is no longer needed. Then add 3 to both sides:

$$x-3 \ge 2$$

$$x \ge 5$$

You can also distribute first to get $2x-6 \ge 4$. Then add 6 to both sides and divide by 2. The answer is the same.

Brackets, fractions, added numbers and coefficients are each undone by the opposite operation, in the same order as for an equation. The one new rule in this section is the flip. The sign flips only when you multiply or divide by a negative number.