Equation Steps Practice Worksheet
Skill 1 of 4 • Foundations
Combine Like Terms: Expressions
Name:
Date: Period:
Strategy: Draw a BOX around variable terms with their sign. Draw a CIRCLE around numbers.
Word Bank: [ Variable • Constant • Combine ]
Problem 1 \(4x + 7 + 2x + 3\)
Step 1: Group \(x\)-terms
Step 2: Group numbers
Simplified:
Problem 2 \(6y + 9 + 3y - 4\)
Step 1: Combine \(y\)-terms
\(6y + 3y =\)
Step 2: Combine numbers
\(9 - 4 =\)
Simplified:
Problem 3 \(8a - 5 - 3a + 12\)
Step 1: Combine \(a\)-terms
\(8a - 3a =\)
Step 2: Combine numbers
\(-5 + 12 = 12 - 5 =\)
Simplified:
Problem 4 \(5m + 4 + 2m + 6 + m\)
Step 1: Clue: \(m = 1m\)! Combine \(m\):
\(5m + 2m + 1m =\)
Step 2: Combine numbers
\(4 + 6 =\)
Simplified:
Skill 1 Check Vault:
\(6x + 10\) \(9y + 5\) \(5a + 7\) \(8m + 10\)
Match each answer
Skill 2 of 4 • Equations
Combine Like Terms to Solve Equations
Name:
Date: Period:
3-Step Plan: 1. Combine like terms on left → 2. Undo + or − → 3. Divide by the coefficient!
Opposite Ops: + ↔ − • × ↔ ÷
Problem 5 \(3x + 2x + 6 = 26\)
Step 1: Combine \(3x + 2x\)
\(x + 6 = 26\)
Step 2: Subtract 6 from both sides
\(5x = 26 - 6 \rightarrow 5x =\)
Step 3: Divide by 5
\(x = 20 \div 5\)
Solution:
\(x =\)
Problem 6 \(7n - 3n + 8 = 24\)
Step 1: Combine \(7n - 3n\)
\(n + 8 = 24\)
Step 2: Subtract 8 from both sides
\(4n = 24 - 8 \rightarrow 4n =\)
Step 3: Divide by 4
\(n = 16 \div 4\)
Solution:
\(n =\)
Problem 7 \(5k + 4 + 2k = 25\)
Step 1: Combine \(5k + 2k\)
\(k + 4 = 25\)
Step 2: Subtract 4 from both sides
\(7k = 25 - 4 \rightarrow 7k =\)
Step 3: Divide by 7
\(k = 21 \div 7\)
Solution:
\(k =\)
Problem 8 \(9w - 4w - 5 = 20\)
Step 1: Combine \(9w - 4w\)
\(w - 5 = 20\)
Step 2: Add 5 to both sides (opposite of -5)
\(5w = 20 + 5 \rightarrow 5w =\)
Step 3: Divide by 5
\(w = 25 \div 5\)
Solution:
\(w =\)
Skill 2 Check Vault:
\(x = 4\) \(n = 4\) \(k = 3\) \(w = 5\)
Match each answer
Skill 3 of 4 • Balances
Equations with Variables on Both Sides
Name:
Date: Period:
Golden Rule: Move the smaller variable term across the “=” sign first using its opposite sign!
Letters to one side • Numbers to other
Problem 9 \(6x + 2 = 2x + 18\)
Step 1: Subtract \(2x\) from both sides
\(6x - 2x =\) \(+ 2 = 18\)
Step 2: Subtract 2 from both sides
\(4x = 18 - 2 \rightarrow 4x =\)
Step 3: Divide by 4
\(x = 16 \div 4\)
Solution:
\(x =\)
Problem 10 \(8y - 5 = 3y + 20\)
Step 1: Subtract \(3y\) from both sides
\(8y - 3y =\) \(- 5 = 20\)
Step 2: Add 5 to both sides
\(5y = 20 + 5 \rightarrow 5y =\)
Step 3: Divide by 5
\(y = 25 \div 5\)
Solution:
\(y =\)
Problem 11 \(4m + 15 = 7m + 3\)
Step 1: Subtract \(4m\) from both sides
\(15 = 7m - 4m + 3 \rightarrow 15 =\) \(+ 3\)
Step 2: Subtract 3 from both sides
\(15 - 3 = 3m \rightarrow\) \(= 3m\)
Step 3: Divide by 3
\(m = 12 \div 3\)
Solution:
\(m =\)
Problem 12 \(9p - 8 = 5p + 16\)
Step 1: Subtract \(5p\) from both sides
\(9p - 5p =\) \(- 8 = 16\)
Step 2: Add 8 to both sides
\(4p = 16 + 8 \rightarrow 4p =\)
Step 3: Divide by 4
\(p = 24 \div 4\)
Solution:
\(p =\)
Skill 3 Check Vault:
\(x = 4\) \(y = 5\) \(m = 4\) \(p = 6\)
Match each answer
Skill 4 of 4 • Mastery
Multi-Step Equations (Distribute & Solve)
Name:
Date: Period:
Multi-Step Order: 1. Distribute (multiply through) → 2. Combine like terms → 3. Solve 2-step equation!
Example: \(3(x + 2) = 3x + 6\)
Problem 13 \(2(x + 5) + 3x = 35\)
Step 1: Distribute 2
\(2 \cdot x + 2 \cdot 5 \rightarrow\) \(2x + 10\) \(+ 3x = 35\)
Step 2: Combine like terms (\(2x + 3x\))
\(x + 10 = 35\)
Step 3: Subtract 10, then divide by 5
\(5x = 25 \rightarrow x = 25 \div 5\)
Solution:
\(x =\)
Problem 14 \(3(2y - 4) + 5 = 29\)
Step 1: Distribute 3
\(3 \cdot 2y - 3 \cdot 4 \rightarrow\) \(6y - 12\) \(+ 5 = 29\)
Step 2: Combine numbers (\(-12 + 5\))
\(6y -\) \(= 29\)
Step 3: Add 7, then divide by 6
\(6y = 36 \rightarrow y = 36 \div 6\)
Solution:
\(y =\)
Problem 15 \(4(w + 3) - 2w = 26\)
Step 1: Distribute 4
\(4 \cdot w + 4 \cdot 3 \rightarrow\) \(4w + 12\) \(- 2w = 26\)
Step 2: Combine like terms (\(4w - 2w\))
\(w + 12 = 26\)
Step 3: Subtract 12, then divide by 2
\(2w = 14 \rightarrow w = 14 \div 2\)
Solution:
\(w =\)
Problem 16 \(5(m - 2) + 4m = 26\)
Step 1: Distribute 5
\(5 \cdot m - 5 \cdot 2 \rightarrow\) \(5m - 10\) \(+ 4m = 26\)
Step 2: Combine like terms (\(5m + 4m\))
\(m - 10 = 26\)
Step 3: Add 10, then divide by 9
\(9m = 36 \rightarrow m = 36 \div 9\)
Solution:
\(m =\)
Skill 4 Check Vault:
\(x = 5\) \(y = 6\) \(w = 7\) \(m = 4\)
Match each answer
