Extending Your Problem Solving Skills
3-8Proof in Algebra
Overview
Justify each step of a solution using a property (commutative, associative, distributive, identity, inverse, substitution).
Key ideas
- Cite a reason for every line of work.
- Use properties of equality (addition, multiplication).
- Builds careful, logical algebra.
Worked examples
Example 1
Problem. Prove: If a + b = c, then a = c − b.
Solution. Start: a + b = c. Add −b: a + b + (−b) = c + (−b) (add. prop. of =). Associative & inverse: a + 0 = c − b. Identity: a = c − b. ∎
Practice
Try each one. Click Show answer when ready.
- 1.
Justify: 4 + (x + 3) = (4 + x) + 3.
- 2.
Justify: 7 + 0 = 7.
- 3.
Justify: 3·(x + 2) = 3x + 6.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Prove: If 3x + 5 = 14, then x = 3.
- 2.
Prove: If a = b and b = c, then a + 2 = c + 2.