Questions and Answers
What is the definition of an equation?
What is a one-step equation?
An equation that requires only one step to solve.
What defines a two-step equation?
An equation that requires two steps to solve.
What is a multi-step equation?
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What is meant by solving literal equations?
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Provide an example of a one-step equation.
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Provide an example of a two-step equation.
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What are the steps for solving a multi-step equation?
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Give an example of a multi-step equation.
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Study Notes
Equations
- Equations express equality between two mathematical expressions using the equal sign (=).
One-step Equations
- These equations require only one operation to solve for the variable.
Two-step Equations
- Involves two operations to find the value of the variable.
Multi-step Equations
- Requires multiple operations to solve, utilizing algebraic rules for simplification.
Formulas and Literal Equations
- Formulas can involve various variables; solving for a different variable is called solving literal equations. For example, the perimeter P of a square can be rearranged to find the side length s from the formula P = 4s.
Examples for One-step Equations
- Example: For x - 6 = -14, adding 6 gives x = -8.
- Example: For -3y = 30, dividing by -3 results in y = -10.
Examples for Two-step Equations
- Simplifying 2/5m + 3 = 2 by subtracting 3 yields 2/5m = -1, leading to m = -5/2 after proper multiplication.
Steps for Solving Multi-step Equations
- Start by distributing and combining like terms.
- Move all variable terms to the left side and numerical values to the right side.
- Solve the resulting one-step equation.
Examples for Multi-step Equations
- For -3(x - 6) + 4(x + 1) = 7x - 10, simplifying leads to combining like terms and solving for x.
- Example: x + 22 = 7x - 10 results in -6x = -32 and simplifies to x = 16/3.
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Description
Test your knowledge on solving equations with this flashcard quiz for Pre-Algebra Chapter 4. Learn key definitions including one-step and two-step equations, and deepen your understanding of how to manipulate mathematical expressions. Perfect for students looking to reinforce their skills in basic algebra.
