Equation Blueprint Worksheet
Equation Blueprint
Multi-Step Equations with Variables on Both Sides
NAME:
DATE:
The 4-Step Blueprint Process
1. DISTRIBUTE
2. COMBINE
3. MOVE VARS
4. ISOLATE
Guided Blueprint Practice
Solve the equations below by completing steps 1 through 4 sequentially in the stacked rows.
Guided Problem 1 \[2(3x - 4) = 4x + 10\]
1. Distribute Multiply the 2 to terms inside.
2. Combine Like Terms Are there like terms on either side?
No like terms to combine. Rewrite equation below.
3. Move Variables Subtract \(4x\) from both sides.
4. Isolate Variable Add 8, then divide by 2.
x = ____
Guided Problem 2 \[-3(2d + 5) + 8d = 3 - 4d\]
1. Distribute Multiply \(-3\) to terms inside.
2. Combine Like Terms Combine \(d\) terms on the left side.
3. Move Variables Add \(4d\) to move variables left.
4. Isolate Variable Add 15, then divide to solve.
d = ____
EQUATION BLUEPRINT WORKSHEET PAGE 1 OF 3
Guided Practice (Continued) Vertical Step Scaffolding
Guided Problem 3 (From Image 5)
\[3(-5y + 2) = 21 - 10y\]
1. Distribute Multiply 3 to terms inside. Watch signs!
2. Combine Like Terms Check both sides for terms to combine.
No like terms to combine. Rewrite equation below.
3. Move Variables Add \(15y\) to both sides to make \(y\) term positive.
4. Isolate Variable Subtract 21, then divide by 5 to solve.
y = ____
Guided Problem 4 (From Image 6)
\[-8(c - 10) = -(c - 3)\]
1. Distribute Distribute \(-8\) on left, \(-1\) on right.
2. Combine Like Terms Check both sides for terms to combine.
No like terms to combine. Rewrite equation below.
3. Move Variables Add \(8c\) to both sides.
4. Isolate Variable Subtract 3, then divide by 7.
c = ____
EQUATION BLUEPRINT WORKSHEET PAGE 2 OF 3
Independent Blueprint
Solve on Your Own • Apply the 4 Steps
6 Problems
Problem 5 \(4(2k - 1) = 2k + 14\)
Show steps
k = _________
Problem 6 \(-2(3x + 4) = 5x - 19\)
Show steps
x = _________
Problem 7 \(5(p - 3) = 2p + 6\)
Show steps
p = _________
Problem 8 \(-3(4m - 2) = -2(5m + 3)\)
Show steps
m = _________
Problem 9 \(6(w + 2) - 4 = 2w + 16\)
Show steps
w = _________
Problem 10 \(-4(z - 1) + 2z = 3(z + 8)\)
Show steps
z = _________
EQUATION BLUEPRINT WORKSHEET PAGE 3 OF 3
Equation Blueprint Answer Key
Equation Blueprint
TEACHER ANSWER KEY & SOLUTION GUIDE
FOR TEACHER REFERENCE
The 4-Step Blueprint Process
1. DISTRIBUTE
2. COMBINE
3. MOVE VARS
4. ISOLATE
Guided Practice Step-by-Step Keys (Vertical)
Detailed mathematical pathways for each step of the vertical graphic organizers.
Guided Problem 1 - Solutions \[2(3x - 4) = 4x + 10\]
1. Distribute Multiply the 2 to terms inside.
\(2(3x) - 2(4) = 4x + 10\)
\(6x - 8 = 4x + 10\)
2. Combine Like Terms Are there like terms on either side?
No like terms to combine.
\(6x - 8 = 4x + 10\)
3. Move Variables Subtract \(4x\) from both sides.
\(6x - 4x - 8 = 10\)
\(2x - 8 = 10\)
4. Isolate Variable Add 8, then divide by 2.
\(2x = 18\)
\(x = 9\)
x = 9
Guided Problem 2 - Solutions \[-3(2d + 5) + 8d = 3 - 4d\]
1. Distribute Multiply \(-3\) to terms inside.
\(-3(2d) + -3(5) + 8d = 3 - 4d\)
\(-6d - 15 + 8d = 3 - 4d\)
2. Combine Like Terms Combine \(d\) terms on the left side.
Combine \(-6d + 8d\) to get \(2d\):
\(2d - 15 = 3 - 4d\)
3. Move Variables Add \(4d\) to move variables left.
\(2d + 4d - 15 = 3\)
\(6d - 15 = 3\)
4. Isolate Variable Add 15, then divide to solve.
\(6d = 18\)
\(d = 3\)
d = 3
EQUATION BLUEPRINT KEY PAGE 1 OF 3
Guided Practice Key (Continued) Image Problems 5 & 6 Solved
Guided Problem 3 (From Image 5)
\[3(-5y + 2) = 21 - 10y\]
1. Distribute Multiply 3 to terms inside. Watch signs!
\(3(-5y) + 3(2) = 21 - 10y\)
\(-15y + 6 = 21 - 10y\)
2. Combine Like Terms Check both sides for terms to combine.
No like terms to combine.
\(-15y + 6 = 21 - 10y\)
3. Move Variables Add \(15y\) to both sides.
\(6 = 21 - 10y + 15y\)
\(6 = 21 + 5y\)
4. Isolate Variable Subtract 21, then divide by 5.
\(-15 = 5y\)
\(y = -3\)
y = -3
Guided Problem 4 (From Image 6)
\[-8(c - 10) = -(c - 3)\]
1. Distribute Distribute \(-8\) on left, \(-1\) on right.
\(-8c + 80 = -c + 3\)
\(-8c + 80 = -c + 3\)
