Always, Sometimes or Never True? · Algebraic Proof

Sort statements about integers and expressions into always true, sometimes true and never true.

Drag each statement into a column (or tap a statement, then a column). Always true: true for every value, so it can be proved. Sometimes true: true for some values and false for others, so give an example of each. Never true: false for every value, so prove that it is false. Try a few values first, then use algebra to decide. Each statement you place correctly shows why when you press Check.

Statements

Always true

Sometimes true

Never true

Then justify each choice in your book: a proof for always true, one example where it is true and one where it is false for sometimes true, and a proof that it can never be true for never true.