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TennesseeMaths

Equations and Inequalities

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you create an equation or inequality from a real-world description, and how do you interpret its solution in context?

Create equations and inequalities in one or more variables from a context and use them to solve problems, interpreting solutions as viable or nonviable (TN A1.A.CED.A.1, A.2, A.3).
A TNReady Algebra I answer on creating equations and inequalities from context (TN A1.A.CED.A.1-3), translating words to symbols, modeling constraints, and judging which solutions are viable.
10 min answer →

How do you rearrange a formula to isolate a chosen variable, treating the other letters as constants?

Rearrange formulas and literal equations to isolate a quantity of interest, using the same reasoning as solving a numerical equation (TN A1.A.CED.A.4).
A TNReady Algebra I answer on rearranging literal equations and formulas (TN A1.A.CED.A.4), isolating a variable, treating other letters as constants, and solving common formulas for a chosen quantity.
9 min answer →

How do you solve simple rational and radical equations, and why can these produce extraneous solutions?

Solve simple rational and radical equations in one variable and explain how extraneous solutions can arise, checking every solution (TN A1.A.REI.A.2).
A TNReady Algebra I answer on solving simple rational and radical equations (TN A1.A.REI.A.2), clearing denominators, squaring both sides, and checking for extraneous solutions.
10 min answer →

How do you solve a linear equation in one variable, and how does each step follow from the properties of equality?

Solve linear equations in one variable, including those with variables on both sides and with coefficients represented by letters, justifying each step (TN A1.A.REI.A.1, A1.A.REI.B.3).
A TNReady Algebra I answer on solving linear equations (TN A1.A.REI.A.1, B.3), the properties of equality, clearing fractions, variables on both sides, and recognizing no-solution and identity cases.
10 min answer →

How do you solve a linear inequality in one variable, and why does multiplying or dividing by a negative flip the inequality?

Solve linear inequalities in one variable and represent the solution on a number line and in interval form, reversing the inequality when multiplying or dividing by a negative (TN A1.A.REI.B.3).
A TNReady Algebra I answer on solving linear inequalities (TN A1.A.REI.B.3), the flip rule for negatives, graphing on a number line with open and closed circles, and compound inequalities.
10 min answer →