Grade 8 - Equations and Inequalities

Students model equations with balance diagrams, interpreting the equal sign relationally and writing one-variable linear equations and inequalities from contexts involving quantities, rates, totals, comparisons, and constraints. They solve one-step and two-step linear equations with integer and rational coefficients using equality-preserving inverse operations, including variables in different positions, and verify solutions by substitution while recognizing when an equation has one, no, or infinitely many solutions. They solve one-step inequalities, reversing the inequality when multiplying or dividing by a negative, and represent rational and compound solution sets symbolically and on number lines with appropriate open or closed endpoints and shaded regions.