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Equations and Inequalities

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you solve absolute-value equations and inequalities, and why do they split into two cases?

Solve absolute-value equations and inequalities in one variable, splitting into two cases and representing solution sets symbolically and on a number line (A.EI.3).
A Virginia SOL Algebra I answer on A.EI.3: isolating the absolute value, splitting into two cases, the and/or distinction for less-than and greater-than inequalities, and recognizing no-solution cases.
9 min answer →

How do you rearrange a literal equation or formula to solve for a specified variable?

Rearrange formulas and literal equations to solve for a specified variable, treating the other letters as constants and using inverse operations (A.EI.1).
A Virginia SOL Algebra I answer on rearranging literal equations and formulas: isolating a chosen variable, treating other letters as constants, clearing fractions, and factoring out the target variable when it appears twice.
9 min answer →

How do you solve multi-step linear equations in one variable, including those with variables on both sides, and identify equations with one, no, or infinitely many solutions?

Solve multi-step linear equations in one variable, including equations with the variable on both sides and with rational-number coefficients, and classify an equation as having one solution, no solution, or infinitely many solutions (A.EI.1).
A Virginia SOL Algebra I answer on A.EI.1: the balance method, clearing fractions, variables on both sides, modeling with linear equations, and identifying one, no, or infinitely many solutions.
9 min answer →

How do you solve linear inequalities in one variable and represent the solution set on a number line?

Solve multi-step linear inequalities in one variable, represent the solution set on a number line and in interval notation, and interpret solutions in context, flipping the inequality when multiplying or dividing by a negative (A.EI.2).
A Virginia SOL Algebra I answer on A.EI.2: solving linear inequalities, the flip rule for multiplying or dividing by a negative, graphing on a number line with open and closed circles, and interpreting solutions in context.
9 min answer →

How do you solve a system of two linear equations by graphing, substitution, and elimination, and what does the number of solutions mean?

Solve systems of two linear equations in two variables by graphing, substitution, and elimination, and interpret one solution, no solution, or infinitely many solutions in context (A.EI.4).
A Virginia SOL Algebra I answer on A.EI.4: solving systems by graphing, substitution, and elimination, classifying one, no, or infinitely many solutions, and modeling situations with a system.
9 min answer →

How do you graph a system of linear inequalities and identify the solution region?

Graph systems of linear inequalities in two variables, identify the overlapping solution region, and determine whether a given point is a solution (A.EI.5).
A Virginia SOL Algebra I answer on A.EI.5: graphing a linear inequality as a half-plane, solid versus dashed boundaries, finding the overlap of a system, and testing whether a point is a solution.
9 min answer →