Variable Quest Worksheet
Variable Quest
IEP Progress Monitoring • Multi-Step Equations
Accuracy Tracker Goal: 80%+
Score: / 6
% Correct:
Student:
Date:
Attempt #:
IEP Goal
Solve multi-step linear equations in one variable requiring distributive expansion, combining like terms, and handling variables on both sides with clean integer coefficients.
PROBLEM 1 Developing
\( 3(x - 4) = 9 \)
Final Answer:
\( x = \)
PROBLEM 2 Developing
\( 7x + 3 = 4x + 18 \)
Final Answer:
\( x = \)
PROBLEM 3 Target
\( 2(3x - 1) - 4x = 10 \)
Final Answer:
\( x = \)
PROBLEM 4 Target
\( 5(x + 2) = 2x - 11 \)
Final Answer:
\( x = \)
PROBLEM 5 Advanced
\( -2(x - 5) + 3x = 4(x + 2) - 1 \)
Final Answer:
\( x = \)
PROBLEM 6 Advanced
\( 3(2x - 4) = -2(x - 6) \)
Final Answer:
\( x = \)
Instructions: Solve each equation. Show your multi-step algebraic operations clearly in the grid boxes. Write your final answer in the slot provided.
FORM-8EE7B-PM1
Variable Quest Answer Key
Variable Quest
Teacher Guide & Key
IEP Progress Monitoring Assessment • CCSS.MATH.CONTENT.8.EE.C.7
Scoring Matrix Goal Target: 5/6 (83%)
1
17%
2
33%
3
50%
4
67%
5
83%
6
100%
PROBLEM 1 (Developing) Answer Key
\( 3(x - 4) = 9 \)
Solution Steps:
1. Distribute 3:
\( 3x - 12 = 9 \)
2. Add 12 to both sides:
\( 3x = 21 \)
3. Divide by 3:
\( x = 7 \)
Correct Answer:
\( x = 7 \)
PROBLEM 2 (Developing) Answer Key
\( 7x + 3 = 4x + 18 \)
Solution Steps:
1. Subtract 4x from both sides:
\( 3x + 3 = 18 \)
2. Subtract 3 from both sides:
\( 3x = 15 \)
3. Divide by 3:
\( x = 5 \)
Correct Answer:
\( x = 5 \)
PROBLEM 3 (Target) Answer Key
\( 2(3x - 1) - 4x = 10 \)
Solution Steps:
1. Distribute 2:
\( 6x - 2 - 4x = 10 \)
2. Combine like terms (6x - 4x):
\( 2x - 2 = 10 \)
3. Add 2 & Divide by 2:
\( 2x = 12 \implies x = 6 \)
Correct Answer:
\( x = 6 \)
PROBLEM 4 (Target) Answer Key
\( 5(x + 2) = 2x - 11 \)
Solution Steps:
1. Distribute 5:
\( 5x + 10 = 2x - 11 \)
2. Subtract 2x from both sides:
\( 3x + 10 = -11 \)
3. Subtract 10 & Divide by 3:
\( 3x = -21 \implies x = -7 \)
Correct Answer:
\( x = -7 \)
PROBLEM 5 (Advanced) Answer Key
\( -2(x - 5) + 3x = 4(x + 2) - 1 \)
Solution Steps:
1. Distribute -2 & expand:
\( -2x + 10 + 3x = 4x + 8 - 1 \)
2. Combine like terms:
\( x + 10 = 4x + 7 \)
3. Subtract x & Subtract 7:
\( 3 = 3x \implies x = 1 \)
Correct Answer:
\( x = 1 \)
PROBLEM 6 (Advanced) Answer Key
\( 3(2x - 4) = -2(x - 6) \)
Solution Steps:
1. Distribute on both sides:
\( 6x - 12 = -2x + 12 \)
2. Add 2x to both sides:
\( 8x - 12 = 12 \)
3. Add 12 & Divide by 8:
\( 8x = 24 \implies x = 3 \)
Correct Answer:
\( x = 3 \)
IEP Progress Monitoring Error Analysis Guide:
Arithmetic Errors:
Calculates wrong sums/products (e.g., \( 3 \times -4 \neq -12 \)), but knows procedural algebra steps.
Sign Rules:
Errors distributing negatives (Problem 4 and 6), or transposing signs when shifting terms across equivalence.
Inverse Operations:
Performs identical operations instead of inverse (e.g., adding to positive or subtracting to negative coefficient).
