• We solve an equation by doing the same operation to both sides, which keeps the two sides equal.
• In this way we isolate the variable on one side:

• Add or subtract the same number on both sides to remove a constant term.
• Multiply or divide both sides by the same number to remove a coefficient.
• Remove brackets first, and simplify each side before solving.
• If there are fractions, multiply both sides by the common denominator.
• If the variable appears on both sides, collect the terms with the variable on one side and the numbers on the other side.

An equation with fractions

• To solve (x + 1) ÷ 2 + x ÷ 3 = 4, multiply both sides by the common denominator 6.
• This gives 3(x + 1) + 2x = 24.
• Remove the bracket to get 3x + 3 + 2x = 24, so 5x = 21 and x = 21 ÷ 5 = 4.2.
• Check: (4.2 + 1) ÷ 2 + 4.2 ÷ 3 = 2.6 + 1.4 = 4.

1. Notice that the solution may be a decimal or a fraction
2. and it does not have to be a whole number.