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FloridaMaths

Linear and Absolute-Value Equations, Inequalities, and Systems

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 and graph the solution set, recognizing the two-case structure and no-solution cases (MA.912.AR.4.1, MA.912.AR.4.2).
A B.E.S.T. Algebra 1 EOC answer on absolute value (MA.912.AR.4), isolating the bars, splitting into two cases, the and versus or structure of inequalities, and identifying no-solution cases.
10 min answer →

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

Solve multi-step linear equations in one variable, including equations with the variable on both sides and with rational-number coefficients, and identify when an equation has one solution, no solution, or infinitely many solutions (MA.912.AR.2.1, MA.912.AR.2.2).
A B.E.S.T. Algebra 1 EOC answer on solving linear equations (MA.912.AR.2), the balance method, clearing fractions, variables on both sides, and identifying one, none, or infinitely many solutions.
9 min answer →

How do you solve and graph linear inequalities in one variable, and why does the inequality sign flip when you multiply or divide by a negative?

Solve multi-step linear inequalities in one variable, graph the solution set on a number line, and interpret it in a real-world context (MA.912.AR.2.4, MA.912.AR.2.5).
A B.E.S.T. Algebra 1 EOC answer on linear inequalities (MA.912.AR.2), solving like equations with the negative-flip rule, graphing on a number line with open and closed circles, and interpreting in context.
9 min answer →

How do you solve a system of two linear equations by graphing, substitution, and elimination, and what do one, none, or infinitely many solutions mean?

Solve systems of two linear equations in two variables by graphing, substitution, and elimination, and interpret the solution, including consistent, inconsistent, and dependent systems (MA.912.AR.9.1, MA.912.AR.9.4).
A B.E.S.T. Algebra 1 EOC answer on systems (MA.912.AR.9), solving by graphing, substitution, and elimination, modeling with two equations, and interpreting one, no, or infinitely many solutions.
11 min answer →

How do you graph a linear inequality in two variables and the solution region of a system of inequalities, and how do you test a point?

Graph linear inequalities in two variables and systems of linear inequalities, identifying the solution region and testing whether a point is a solution, including in real-world constraint contexts (MA.912.AR.9.6).
A B.E.S.T. Algebra 1 EOC answer on systems of inequalities (MA.912.AR.9), dashed versus solid boundaries, shading the correct half-plane, the overlap region for a system, and testing a point.
10 min answer →

How do you find the slope and intercepts of a line, write its equation in slope-intercept and point-slope form, and graph it?

Determine the slope and intercepts of a linear function, write its equation in slope-intercept, point-slope, and standard form, and graph it, including parallel and perpendicular lines (MA.912.AR.2.3, MA.912.AR.3.1).
A B.E.S.T. Algebra 1 EOC answer on linear functions (MA.912.AR.2, AR.3), the slope formula, slope-intercept and point-slope forms from the reference sheet, graphing, and parallel and perpendicular slopes.
11 min answer →