Simple Equations: 20 flashcards
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1. What is a simple equation?
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An equation where the unknown appears only to the first power, with no products of unknowns and no unknowns in denominators.
2. What is the general form of a simple equation in one variable?
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$ax + b = c$ with $a \neq 0$.
3. State the balance model for solving equations.
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Whatever operation you apply to one side of an equation, you must apply the same operation to the other side.
4. What does 'solving an equation' mean?
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Isolating the unknown on one side using inverse operations.
5. In what order should you undo operations applied to the unknown?
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Undo operations in reverse order of how they were applied to the unknown.
6. What is transposition?
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Moving a term from one side of an equation to the other and flipping its sign — a shortcut for adding or subtracting the same term on both sides.
7. How do you handle an equation where the unknown appears on both sides?
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Collect unknowns on one side and constants on the other, then divide by the coefficient.
8. What is the final step when solving $ax = b$?
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Divide both sides by the coefficient $a$ to get $x = b/a$.
9. Why should you always check your solution?
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Substituting the value back into the original equation confirms it is correct and catches sign or operation errors.
10. What is the difference between an expression and an equation?
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An expression has no equals sign and is simplified; an equation has an equals sign and is solved.
11. How do you translate 'seven more than twice a number is 19' into an equation?
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$2x + 7 = 19$.
12. What keywords in a word problem suggest addition?
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Words like 'more than', 'increased by', 'sum'.
13. What keyword signals the equals sign in a word problem?
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The word 'is'.
14. What is a common mistake when applying an operation to an equation?
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Forgetting to apply the operation to every term, not just the one you are focused on.
15. Why is dividing too early often a bad idea?
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It can make the equation messier; it is usually cleaner to collect terms first.
16. What does the word 'simple' in 'simple equation' refer to?
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It refers to the degree of the unknown being 1, not to how easy the equation is.
17. Solve $2x + 5 = 11$.
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$x = 3$.
18. Solve $5x - 3 = 2x + 9$.
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$x = 4$.
19. What is the first step to solve $3x + 4 = 19$?
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Subtract 4 from both sides to get $3x = 15$.
20. Why is checking your answer in the original equation important?
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Because a solution is correct only if it satisfies the original equation, not a modified version.
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