One-Step Equations with Variables
Grade 5 equations introduce variables explicitly: 4 + X = 15 instead of 4 + ? = 15. The variable is a more powerful notation because it can appear in multi-step equations and expressions. Solving by inverse operations remains the strategy: if X is added by 4, subtract 4 from both sides. The verification step is non-negotiable: substitute X = 11 into 4 + X = 15 to confirm 4 + 11 = 15. This habit, built in Grade 5, pays dividends through all of algebra.
Variable notation
4 + X = 15 means: what number, when 4 is added, gives 15? The variable X names the unknown quantity. Solving: subtract 4 from both sides: X = 15 - 4 = 11. The balance model: whatever you do to one side, do to both. Taking 4 away from the left side: the 4 and the +4 cancel, leaving X alone.
All four operations
Addition: X + 7 = 23, so X = 23-7 = 16. Subtraction: 30 - X = 12, so X = 30-12 = 18. Multiplication: 6X = 42, so X = 42/6 = 7. Division: X/4 = 9, so X = 9x4 = 36. Each equation type uses the inverse operation. Recognizing which operation is applied to X determines which inverse to use.
Word problems to equations
A community gathering needs 4 times as many chairs as there are tables. If there are 60 chairs, how many tables? Equation: 4X = 60. X = 60/4 = 15 tables. Translating from words to equations is the key competency: identify the unknown, name it X, express the given relationship as an equation, solve, verify.