Equation Mission Worksheet
Math Practice Series
Equation Mission
Isolate the variable and solve the multi-step challenge below.
Mission ID LEVEL-1-A
Student Name
Date
Class Period
The Target Solve for the unknown variable \(y\) step-by-step.
\(2(-4y + 3) = 3 - 7y\)
Show Your Algebraic Steps Keep each step aligned and neat
Mission Checklist
Distribute cleanly
Gather variable terms
Isolate the constant
Verify the solution
Final Code Solution
y =
Equation Mission Answer Key
Teacher Resource • Answer Key
Equation Mission Key
Complete pedagogical breakdown, solution steps, and key student misconceptions.
Status RESOLVED
Target Concept: Distributive property, variable collection, isolation of constants on both sides.
Target Solution: \(y = 3\) (Positive Whole Number)
Step-by-Step Exemplar Pathway Perfect score solution guide
1
Distributive Property
\(-8y + 6 = 3 - 7y\)
⚠️ Common Trap: Students often forget to distribute the coefficient \(2\) to the constant \(3\), mistakenly writing \(-8y + 3\) instead of \(-8y + 6\).
2
Gather Variable Terms
\(6 = 3 + y\)
💡 Strategy Choice: Adding \(8y\) to both sides is recommended to keep the variable's coefficient positive, bypassing the step of multiplying or dividing by \(-1\).
3
Isolate Variable
\(3 = y\) or \(y = 3\)
🔧 Balance Check: Confirm that students perform the same operation (subtracting \(3\)) on both sides of the equation to preserve equivalent values.
Verification Proof (Check Your Work)
Substitute \(y = 3\) back into the original equation:
Left Hand Side (LHS) \(2(-4(3) + 3) = 2(-12 + 3)\)
\(= 2(-9) = \mathbf{-18}\)
Right Hand Side (RHS) \(3 - 7(3) = 3 - 21\)
\(= \mathbf{-18}\)
Pedagogical Tip
Encourage students to verbally narrate each operational change they execute. Prompt them to check their answer directly to confirm correctness immediately.
Verified Solution
y =
3
