Conditions on Coefficients: Identity, Degree, No Solution

Some conditions are about the shape of an equation or inequality, not its solution. 'True for every x' means the two sides are the same polynomial, so matching coefficients gives the unknowns; 'linear' means the square term's coefficient is zero while the first-degree coefficient is not; 'no solution' means the x terms cancel to 0 * x and what is left is false -- 0 * x equal to a nonzero number in an equation, or a constant inequality that fails in an inequality. The move is to collect like terms and read the condition off the coefficients.

grade 7–8 Expressions Convert to AlgebraEliminate Possibilities

Builds on: Say It in Letters

Progression (6)

g9 1. Linear means the square term's coefficient is zero AExpressions · foundational

g8 2. True for every k means an identity in k Expressions · foundational

g8 3. No solution means 0 times x equals a nonzero number ExpressionsRatios · core

g9 4. Match coefficients of like terms AExpressions · core

g8 5. Pair each monomial with a term by degree Expressions · advanced

g8 6. No solution forces a zero coefficient Expressions · advanced