➕ Algebra 1 · Equations
Solving Two-Step Equations: fun ways and memory help
The same idea, the fun way
Pick the one that clicks. Each one explains the same concept from a different angle.
Fair is fair
In a fair deal, whatever happens to one side happens to the other. If you and a friend each start with the same number of pizza slices and you each eat 3, you are still even.
How it connects: An equation is a fairness contract. Whatever you do to one side, do to the other, and it stays balanced.
Back to the Future
In Back to the Future, Marty accidentally changes one event in the past and has to set it right before he can get home to 1985. To fix a change, you have to know exactly what was changed.
How it connects: Solving for x is like setting the timeline right: figure out exactly what was done to x, then undo it, last change first.
Scooby-Doo unmasking
In nearly every episode, the “monster” turns out to be a person in disguise. Imagine a villain who put on a costume first and a mask last. To unmask them, the mask comes off first, then the costume.
How it connects: In 2x + 3 = 11, the +3 is the mask, put on last. Take it off first (subtract 3), then the ×2 (divide by 2), and the unknown is unmasked.
Don’t put the cart before the horse
The proverb means doing things in the wrong order makes everything harder.
How it connects: You can divide first, but then you must divide every term, and it gets messy. Undo the adding or subtracting first and the cart follows the horse.
Get to the bottom of it
To “get to the bottom of it” means to dig through everything until you find the real answer.
How it connects: Solving an equation is getting to the bottom of what x really is, peeling away what is stuck to it one layer at a time.
Ctrl + Z
The undo button reverses your most recent action first, then the one before it. It never skips ahead.
How it connects: Inverse operations work the same way. Undo the last thing that happened to x first.
The humble equal sign
Why was the equal sign so humble? Because it knew it wasn’t less than or greater than anyone else.
How it connects: Both sides of an equation are equal, so whatever you do to one side you do to the other.
Memory help
SADMEP: PEMDAS backward
To undo, run PEMDAS in reverse: Subtract/Add first, then Divide/Multiply, then Exponents, then Parentheses. For equations shaped like ax + b = c you only need the first two. Say it as: “Silly Aliens Dance, Moonwalk, Eat Pizza.”
The undo rhyme
Add or subtract, that’s step one. Multiply or divide, then you’re done. Both sides, always, keep it fair. Check your answer, show you care.
The gift wrapper
A gift is wrapped by putting it in a box first and tying the ribbon last. To open it, you do the reverse: ribbon off first, then the box. In 2x + 3, the multiply is the box and the +3 is the ribbon. Ribbon first, then box.
See the seesaw
Picture a seesaw with 2x + 3 on one side and 11 on the other. Every move you make, a ghost copy of that move happens on the other side. If you can’t picture the ghost, you probably forgot one.
Walk through your home
Walk in your front door: that is Step 1, undo add/subtract. Go down the hall to the kitchen: Step 2, undo multiply/divide. Open the fridge and look inside to check the answer. Three stops, one for each step.
The sign belongs to the number on its right
In x − 4 = 3, the constant is negative 4 (4 is being subtracted), so you add 4 to both sides. Say it out loud: “minus 4 means I owe 4, so I pay back 4.”