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 have a mystery box of donuts. You know the box plus 2 extra donuts equals 12 donuts total. How many are in the box? If you guessed 10, congratulations! You just did algebra! 🍩
In math, a linear equation is basically just a fun mystery puzzle. Instead of a physical box, mathematicians use letters like or to hide the secret number. The equal sign is like a perfectly balanced seesaw on a playground. Whatever is sitting on the left side of the seesaw must weigh exactly the same as whatever is sitting on the right side. ⚖️
On the SSAT, you get to be the ultimate math detective! Your main job is to get the mystery letter all by itself so you can figure out its true identity. To do this, you just use the exact opposite math of what you see. If the equation shows addition, you use subtraction to undo it! If you see multiplication, you use division! It's like walking backward to retrace your steps. Just remember the most important rule of the playground: Whatever you do to one side of the seesaw, you absolutely MUST do to the other side to keep it perfectly balanced. Let's grab our magnifying glasses and crack some secret codes! 🕵️♂️
Practice Questions
5 practice questions for SSAT Middle Level
What is the solution to the equation above?
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- To solve for , first subtract from both sides of the equation: . Next, subtract from both sides: . Finally, divide by to isolate : .
Which of the following is equivalent to the expression above?
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- First, distribute the negative sign to each term in the second expression: . Then, combine the like terms with the first expression: .
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- Three times the length is . Four feet less than this amount is . Distribute the 3 to get . Combine the constant terms to get .
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- To solve for , multiply the numerator and denominator of by 3 to create a common denominator of 15. This gives . Since the denominators are equal, the numerators must be equal: . Subtracting 1 from both sides gives . Alternatively, you can cross-multiply: .
What is the value of in the equation above?
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- First, distribute the 2 on the left side of the equation: . Next, subtract from both sides to group the variables: . Finally, add 11 to both sides to solve for : .
Tips & Strategies
- Use the answers to cheat (legally)! If you're stuck on an equation, try plugging the multiple-choice answers back into the spot to see which one makes the equation perfectly balanced.
- Write down every single step. Trying to juggle numbers in your head is like trying to carry 10 pizzas without a box—something will drop! Write your steps neatly on your scratch paper.
Common Mistakes
- Watch out for doing the opposite operation on only ONE side! If you add to the left, you MUST add to the right, or your math seesaw will crash.
- Don't forget to answer the actual question! Sometimes you'll find , but the SSAT asks for . Always read the final question one last time before bubbling!
Frequently Asked Questions
Do I need to be able to do this in my head?
Nope! In fact, doing algebra in your head is a trap. The SSAT gives you plenty of scratch paper, so always write out your steps to avoid silly mistakes.
What if I forget the opposite of multiplication or division?
Just think of them as best friends! Multiplication and division undo each other. Addition and subtraction undo each other.
Are linear equations on the Lower, Middle, or Upper level SSAT?
You'll see simple one-step equations on the Lower level, and more two-step equations on the Middle and Upper levels. They are a huge part of the test!