Linear Expressions & Equations
Writing, simplifying, and evaluating algebraic expressions, and solving single-variable linear equations — excludes systems (see systems-of-equations), inequalities (see inequalities), and polynomial/radical expressions (see polynomials-quadratics, radical-rational-expressions)
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Imagine you are a secret agent trying to crack a safe. In math, solving equations is just like being a detective! You are looking for a mystery number, usually hiding behind a letter like . 🕵️♂️
Think of an equation like a perfectly balanced seesaw at the playground. The equal sign is the exact middle of the seesaw. Whatever you do to one side, you absolutely must do to the other side to keep it from crashing down. If you take away 5 slices of pizza from the left side, you have to take away 5 slices of pizza from the right side! 🍕⚖️
On the ISEE, you will see questions called "Linear Equations." That is just a fancy math term for finding that missing number. Your mission is to get all by itself on one side of the equal sign. How? By using opposite actions! If a number is added to , you subtract it. If a number is multiplied by , you divide it. You are basically peeling away the extra numbers layer by layer, just like peeling an onion (but without the tears!). 🧅
Whether you are taking the Mathematics Achievement section or looking at Column A and Column B in the Quantitative Reasoning section, just remember your golden rule: Keep the seesaw balanced! You've got this! Let's solve some mysteries. 🚀
Practice Questions
4 practice questions for ISEE Lower Level
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- The correct answer is (B), . Sarah bought 3 notebooks at $4 each, which is represented mathematically as . Adding the unknown cost of the pack of pens () gives her total of $17. This can be written as the equation .
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- The correct answer is (B). "3 times a number" is written as . "5 less than" means subtracting 5 from that amount, giving . On the other side of the equation, "7 more than the number" means adding 7 to , giving . Setting them equal results in .
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- The correct answer is (C). First, think about what number multiplied by 3 equals 15. Since , the value inside the parentheses, , must equal 5. So, . By adding 2 to both sides, we find that .
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- The correct answer is (A). "Twice the number of marbles that Leo has" is written algebraically as . "4 more than" means adding 4 to that amount, giving . Since we know Mark's total is 20 marbles, we set the expression equal to 20: .
Tips & Strategies
- For Quantitative Comparison questions, don't just guess! Actually solve both mini-equations for and before comparing them. It only takes a few extra seconds.
- Plug your answer back in! If you find that , put 5 back into the original equation to see if it makes sense. It's a built-in way to check your work on the ISEE Mathematics Achievement section!
- Remember PEMDAS in reverse! When solving for , undo addition and subtraction first, then undo multiplication and division. Peel the onion from the outside in!
Common Mistakes
- Watch out for negative signs! If you have and divide by , the answer is , not . Dropping a negative sign is the most common trap on the ISEE.
- Don't forget the Golden Rule: If you add or subtract a number on the left side, you MUST do it to the right side too. Don't let your seesaw crash!
Frequently Asked Questions
What if I get stuck and can't solve the equation?
Since the ISEE is multiple choice, you can use a trick called 'plugging in'! Just take the answer choices (A, B, C, D) and plug them into the equation for to see which one works perfectly.
Is there a penalty if I guess wrong on the ISEE?
Nope! The ISEE does not have a guessing penalty. If you are running out of time or completely stuck, make sure to pick an answer for every single question.
What if there are variables on both sides of the equation?
No problem! First, move all the terms to one side by adding or subtracting. For example, in , subtract from both sides to get , then solve as usual.
What's the difference between Quantitative Reasoning and Mathematics Achievement?
Quantitative Reasoning asks you to think logically, like comparing Column A and Column B. Mathematics Achievement is more like the math tests you take in school, where you calculate a specific answer to a problem.