One Step Equations Worksheet
Level 1 • Foundations Grades 3–6
One-Step Equations
Score
____ / 10
Name: ______________________
Date: ______________
Class/Period: __________
Directions: Solve for the variable by using inverse operations. Keep the equation balanced.
Inverse: \(+\leftrightarrow -\), \(\times\leftrightarrow \div\)
1 \(x + 7 = 19\)
Addition
\(x =\)
2 \(y - 12 = 15\)
Subtraction
\(y =\)
3 \(4m = 36\)
Multiplication
\(m =\)
4 \(\frac{n}{5} = 8\)
Division
\(n =\)
5 \(a + 28 = 53\)
Addition
\(a =\)
6 \(p - 19 = 24\)
Subtraction
\(p =\)
7 \(7w = 56\)
Multiplication
\(w =\)
8 \(\frac{k}{6} = 9\)
Division
\(k =\)
9 \(14 + t = 42\)
Addition
\(t =\)
10 \(8b = 96\)
Multiplication
\(b =\)
Quick Check: Substitute your answer back into the equation to verify that both sides are equal!
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Two Step Equations Worksheet
Level 2 • Intermediate Grades 6–7
Two-Step Equations
Score
____ / 10
Name: ______________________
Date: ______________
Class/Period: __________
Directions: Isolate the variable term first, then isolate the variable using inverse operations.
Order: Undo \(+\) or \(-\) first, then \(\times\) or \(\div\)
1 \(2x + 5 = 17\)
Step 1: - 5
\(x =\)
2 \(3y - 8 = 13\)
Step 1: + 8
\(y =\)
3 \(\frac{m}{4} + 6 = 11\)
Step 1: - 6
\(m =\)
4 \(5n - 14 = 31\)
Step 1: + 14
\(n =\)
5 \(\frac{p - 3}{2} = 8\)
Step 1: \(\times 2\)
\(p =\)
6 \(4a + 15 = 47\)
Step 1: - 15
\(a =\)
7 \(\frac{w}{3} - 7 = 5\)
Step 1: + 7
\(w =\)
8 \(6k + 9 = 45\)
Step 1: - 9
\(k =\)
9 \(7t - 16 = 26\)
Step 1: + 16
\(t =\)
10 \(2(x + 4) = 22\)
Step 1: \(\div 2\) or expand
\(x =\)
Pro Tip: Think of the balance scale: whatever operation you perform on the left side, do exactly the same to the right side!
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Multi Step Equations Worksheet
Level 3 • Advanced Grades 7–8
Multi-Step Equations
Score
____ / 10
Name: ______________________
Date: ______________
Class/Period: __________
Directions: 1. Distribute • 2. Combine like terms • 3. Move variables to one side • 4. Solve.
Simplify first!
1 \(3x + 4 + 2x = 29\)
Like Terms
\(x =\)
2 \(4(y - 2) + 5 = 25\)
Distribute
\(y =\)
3 \(6m - 14 = 2m + 18\)
Both Sides
\(m =\)
4 \(5(n + 2) - 8 = 32\)
Distribute
\(n =\)
5 \(7p - 3p + 11 = 35\)
Like Terms
\(p =\)
6 \(3(2a + 4) = 30\)
Distribute
\(a =\)
7 \(8w - 5 = 3w + 25\)
Both Sides
\(w =\)
8 \(2(4k - 3) = 3k + 24\)
Both Sides
\(k =\)
9 \(9t - 4(t - 2) = 38\)
Sign Alert
\(t =\)
10 \(5(x - 3) = 2(x + 6)\)
Distribute Both
\(x =\)
Watch the Negative: Distributing \(-4(t - 2)\) gives \(-4t + 8\). Pay special attention to sign changes!
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Equation Escalation Answer Key
Teacher Master Guide Grades 3–8 Solutions
Equation Escalation • Answer Key
All 30 Solutions • 3 Levels
Quick-reference answer key showing primary algebraic steps and final verified values for fast grading and diagnostic review.
1-Step Equations 10 Pts
1. \(x + 7 = 19\) x = 12
2. \(y - 12 = 15\) y = 27
3. \(4m = 36\) m = 9
4. \(\frac{n}{5} = 8\) n = 40
5. \(a + 28 = 53\) a = 25
6. \(p - 19 = 24\) p = 43
7. \(7w = 56\) w = 8
8. \(\frac{k}{6} = 9\) k = 54
9. \(14 + t = 42\) t = 28
10. \(8b = 96\) b = 12
2-Step Equations 10 Pts
1. \(2x + 5 = 17\) x = 6
\(2x=12\)
2. \(3y - 8 = 13\) y = 7
\(3y=21\)
3. \(\frac{m}{4} + 6 = 11\) m = 20
\(\frac{m}{4}=5\)
4. \(5n - 14 = 31\) n = 9
\(5n=45\)
5. \(\frac{p - 3}{2} = 8\) p = 19
\(p-3=16\)
6. \(4a + 15 = 47\) a = 8
\(4a=32\)
7. \(\frac{w}{3} - 7 = 5\) w = 36
\(\frac{w}{3}=12\)
8. \(6k + 9 = 45\) k = 6
\(6k=36\)
9. \(7t - 16 = 26\) t = 6
\(7t=42\)
10. \(2(x + 4) = 22\) x = 7
\(x+4=11\)
Multi-Step Equations 10 Pts
1. \(3x+4+2x=29\) x = 5
\(5x+4=29 \rightarrow 5x=25\)
2. \(4(y-2)+5=25\) y = 7
\(4y-3=25 \rightarrow 4y=28\)
3. \(6m-14=2m+18\) m = 8
\(4m=32\)
4. \(5(n+2)-8=32\) n = 6
\(5n+2=32 \rightarrow 5n=30\)
5. \(7p-3p+11=35\) p = 6
\(4p+11=35 \rightarrow 4p=24\)
6. \(3(2a+4)=30\) a = 3
\(6a+12=30 \rightarrow 6a=18\)
7. \(8w-5=3w+25\) w = 6
\(5w=30\)
8. \(2(4k-3)=3k+24\) k = 6
\(8k-6=3k+24 \rightarrow 5k=30\)
9. \(9t-4(t-2)=38\) t = 6
\(5t+8=38 \rightarrow 5t=30\)
10. \(5(x-3)=2(x+6)\) x = 9
\(5x-15=2x+12 \rightarrow 3x=27\)
Grading Rubric Suggestion: Give 1 point for showing correct inverse operation / simplification steps and 1 point for correct final variable value (total 2 pts per question or scaled to 10 pts).
Frequent Student Misconceptions: Level 2: forgetting to apply inverse operations to both sides. Level 3: forgetting to distribute negative signs across both terms inside parentheses.
Equation Escalation Teacher Resource Suite Master Answer Sheet
