Grade 10 - Linear Equations and Inequalities

Students solve one-variable linear equations with integer, decimal, and fractional coefficients by distributing, combining like terms, and applying inverse operations, including equations with variables on both sides. They distinguish one solution, no solution from contradictions such as $0=5$, and infinitely many solutions from identities such as $0=0$, while rearranging linear formulas to isolate a variable and solving one-variable linear inequalities, reversing the inequality when multiplying or dividing by a negative and representing solution sets on number lines or in interval notation. They model contextual relationships with linear equations and inequalities, preserving units and domain restrictions and interpreting solutions as exact values, bounds, or feasible ranges.