Algebra 1
Solving Linear Equations flashcards
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- What does inverse operations mean?One-Step and Two-Step Equations
- An operation that reverses another operation.
- Why perform the same operation on both sides?One-Step and Two-Step Equations
- To keep the equation balanced.
- How would you define one-step equations?One-Step and Two-Step Equations
- An equality solved with one inverse operation.
- How can a candidate solution be checked?One-Step and Two-Step Equations
- Substitute it into the original equation.
- What is meant by two-step equations?One-Step and Two-Step Equations
- An equation requiring two inverse operations in the standard form ax+b=d.
- Why remove b before dividing in ax+b=d?One-Step and Two-Step Equations
- It isolates the term containing x.
- What does distribution before solving mean?Multi-Step Equations
- Applying a factor to every term inside a sum.
- Why distribute before combining terms?Multi-Step Equations
- The variable terms become visible.
- How would you define combining like terms?Multi-Step Equations
- Reducing like variable terms to one equivalent term.
- What cannot be combined as like terms?Multi-Step Equations
- Terms with different variable powers.
- What is meant by checking multi-step solutions?Multi-Step Equations
- Testing a candidate in the untransformed equation.
- Why check the original equation?Multi-Step Equations
- An earlier sign or distribution error may have changed the work.
- What does collecting variable terms mean?Variables on Both Sides
- Using equivalent operations to gather variable terms.
- Why keep the equality balanced?Variables on Both Sides
- Unequal operations change the equation.
- How would you define one solution?Variables on Both Sides
- Exactly one real number satisfies the equation.
- How can a single solution be verified?Variables on Both Sides
- Substitute it into both original sides.
- What is meant by identity and contradiction?Variables on Both Sides
- An identity is always true; a contradiction is never true.
- What does 0=5 mean for the original equation?Variables on Both Sides
- There is no solution if the transformations were equivalent.
- What does isolating a symbol mean?Literal Equations and Formulas
- Rearranging a formula to express one symbol in terms of others.
- What should be stated when dividing by a symbol?Literal Equations and Formulas
- That the divisor is nonzero.
- How would you define units in formulas?Literal Equations and Formulas
- A relationship among quantities with defined units.
- Why label the solved variable?Literal Equations and Formulas
- To interpret its value and units correctly.
- What is meant by formula substitution?Literal Equations and Formulas
- Replacing known symbols in a formula and calculating.
- Why check the original formula?Literal Equations and Formulas
- It verifies the rearrangement and arithmetic.
- What does defining the unknown mean?Equation Word Problems
- A chosen symbol representing a contextual quantity.
- Why include units in a definition?Equation Word Problems
- They make the model interpretable.
- How would you define fixed fees and rates?Equation Word Problems
- A constant charge combined with a per-unit charge.
- Which part changes with item count?Equation Word Problems
- The rate times the number of items.
- What is meant by contextual reasonableness?Equation Word Problems
- Checking a computed value against real-world restrictions.
- Why reject a negative item count?Equation Word Problems
- An item count cannot be negative in this context.