Equation Reasoners Worksheet
Algebra I • Guided Support
Reasoning with Equations
Name:
Date:
Period:
Operation Clue Words
+ Add: sum, more than
− Subtract: difference, less than
× Multiply: product, times, twice (\(2n\))
÷ Divide: quotient, divided by
The Golden Rule of Equations
Equations remain EQUIVALENT if you do the exact same operation to BOTH sides of the equal sign.
PART 1: Translate Words to Expressions Tip: Use \(n\) or \(x\) for "a number"
MODEL "5 less than twice a number" → twice a number (\(2n\)) minus 5
\(2n - 5\)
1. The sum of a number and 12
Clue word: sum (+)
Expression:
2. The quotient of a number and 8
Clue word: quotient (÷ or fraction)
Expression:
3. Three more than one-half of a number
Clue words: one-half (\(\frac{1}{2}n\)), more than (+)
Expression:
PART 2: Explore — Are They Equivalent? Equivalent means both equations share the same solution
CASE 1
Equation A: \(6x + 12 = 24\)
Equation B: \(6x + 12 = 12\)
1. What changed between A and B?
The right side subtracted 12 (\(24 - 12 = 12\)).
2. Was 12 subtracted from BOTH sides?
Yes
No (only right side)
Are A and B equivalent?
YES NO
CASE 2
Equation A: \(4x - 8 = 12\)
Equation B: \(x - 2 = 3\)
1. What changed between A and B?
Every single term was divided by 4.
2. Was 4 divided from BOTH sides?
Yes (both sides ÷ 4)
No
Are A and B equivalent?
YES NO
Rule to Remember: To create an equivalent equation, you must apply the same operation to
Complete:
Algebra I • Page 1 of 2 • Reasoning with Linear Equations
Guided Practice & Error Analysis
Name:
PART 3: Error Analysis — What Went Wrong? Spot the Algebra Mistake
A student tried to simplify the equation: \(6x + 2 = 14 \;\longrightarrow\; x + 2 = 14\)
Step 1: Check what the student did.
The student divided \(6x\) by \(6\) to get \(x\). Did they divide the other terms by 6?
Yes, they divided everything by 6.
No, they only divided \(6x\), not both sides.
Step 2: Fix the mistake.
If you divide the entire equation \(6x + 2 = 14\) by 2, write the true equivalent equation:
PART 4: Check for Equivalence Test if the balance is kept
1. Pair A: \(10x - 5 = 25\) and \(2x - 1 = 5\)
Hint: Divide all terms by 5. (\(10\div 5=2\), \(5\div 5=1\), \(25\div 5=5\))
Are they equivalent?
YES NO
2. Pair B: \(3x + 9 = 18\) and \(3x = 12\)
Hint: Left side subtracted 9 (\(9-9=0\)). What is \(18 - 9\)? Is it 12?
Are they equivalent?
YES NO
3. Which action will transform \(3x + 9 = 12\) into an equivalent equation?
Subtract 9 from only the left side
Divide both sides by 3
Multiply only the left side by 3
Add 4 to only the right side
PART 5: Solve & Explain Your Balance Step Equation: \(4x - 6 = 14\)
Step
Show Your Work
What did you do to BOTH sides?
Step 1: Undo − 6
"I added to BOTH sides."
Step 2: Undo × 4
"I divided BOTH sides by ."
Algebra I • Page 2 of 2 • Reasoning with Linear Equations
