One Step Equation Worksheets - Free Printable
Educational worksheet: One Step Equation Worksheets. Download and print for classroom or home learning activities.
PNG
200×260
3.8 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1526000
⭐
Show Answer Key & Explanations
Step-by-step solution for: One Step Equation Worksheets
▼
Show Answer Key & Explanations
Step-by-step solution for: One Step Equation Worksheets
Let’s solve each one-step equation step by step. Remember: to solve for the variable, we need to “undo” what’s being done to it — using the opposite operation.
---
1) -9x = -18
We want to get x alone. Right now, x is multiplied by -9. So we divide both sides by -9.
→ x = (-18) ÷ (-9)
→ x = 2
✔ Check: -9 × 2 = -18 → Correct!
---
2) (5/6) + q = 1 1/3
First, convert mixed number to improper fraction:
1 1/3 = 4/3
So:
(5/6) + q = 4/3
Subtract 5/6 from both sides:
q = 4/3 - 5/6
Find common denominator (6):
4/3 = 8/6
So:
q = 8/6 - 5/6 = 3/6 = 1/2
✔ Check: 5/6 + 1/2 = 5/6 + 3/6 = 8/6 = 4/3 = 1 1/3 → Correct!
---
3) (7/9)t = -6
t is multiplied by 7/9. To undo that, multiply both sides by the reciprocal: 9/7.
t = -6 × (9/7) = -54/7
That’s an improper fraction. We can leave it like this or write as mixed number: -7 5/7
But since the problem doesn’t specify, we’ll keep it as -54/7.
✔ Check: (7/9) × (-54/7) = -54/9 = -6 → Correct!
---
4) t / 10 = -3
t is divided by 10. Multiply both sides by 10.
t = -3 × 10 = -30
✔ Check: -30 ÷ 10 = -3 → Correct!
---
5) -0.7 + s = 6.2
Add 0.7 to both sides to isolate s.
s = 6.2 + 0.7 = 6.9
✔ Check: -0.7 + 6.9 = 6.2 → Correct!
---
6) (2/3)z = -18
Multiply both sides by reciprocal of 2/3 → which is 3/2.
z = -18 × (3/2) = -54/2 = -27
✔ Check: (2/3) × (-27) = -54/3 = -18 → Correct!
---
7) a - 3.5 = -99
Add 3.5 to both sides.
a = -99 + 3.5 = -95.5
✔ Check: -95.5 - 3.5 = -99 → Correct!
---
8) y / (2/5) = 4/5
Dividing by a fraction? That’s same as multiplying by its reciprocal.
So: y × (5/2) = 4/5
Now multiply both sides by 2/5 to isolate y.
y = (4/5) × (2/5) = 8/25
Wait — let me double-check.
Actually, if y ÷ (2/5) = 4/5, then:
y = (4/5) × (2/5)? No — that’s wrong.
Correct way:
If y ÷ (2/5) = 4/5, then y = (4/5) × (2/5)? NO!
Division by fraction:
y ÷ (2/5) = y × (5/2)
So: y × (5/2) = 4/5
Then multiply both sides by 2/5:
y = (4/5) × (2/5) = 8/25? Wait — no:
To isolate y, multiply both sides by 2/5:
y = (4/5) × (2/5)? Let's think again.
Equation:
y × (5/2) = 4/5
Multiply both sides by 2/5:
y = (4/5) × (2/5) = 8/25? But that would be if we multiplied by 2/5 on right side.
Wait — actually:
Left side: [y × (5/2)] × (2/5) = y × (5/2 × 2/5) = y × 1 = y
Right side: (4/5) × (2/5) = 8/25
So yes, y = 8/25
✔ Check: (8/25) ÷ (2/5) = (8/25) × (5/2) = 40/50 = 4/5 → Correct!
---
9) -4 = g / (8/3)
Same idea: g divided by 8/3 equals -4.
So: g = -4 × (8/3) = -32/3
Or as mixed number: -10 2/3
✔ Check: (-32/3) ÷ (8/3) = (-32/3) × (3/8) = -96/24 = -4 → Correct!
---
10) 6.1b = 2.44
Divide both sides by 6.1.
b = 2.44 ÷ 6.1
Let’s calculate:
2.44 ÷ 6.1 = ?
Multiply numerator and denominator by 100 to eliminate decimals:
244 ÷ 610
Simplify: divide numerator and denominator by 2 → 122 / 305
Check if divisible further? 122 ÷ 2 = 61, 305 ÷ 5 = 61 → wait:
Actually, 2.44 ÷ 6.1 = 0.4
Because 6.1 × 0.4 = 2.44
Yes!
✔ Check: 6.1 × 0.4 = 2.44 → Correct!
---
Final Answer:
1) x = 2
2) q = 1/2
3) t = -54/7
4) t = -30
5) s = 6.9
6) z = -27
7) a = -95.5
8) y = 8/25
9) g = -32/3
10) b = 0.4
---
1) -9x = -18
We want to get x alone. Right now, x is multiplied by -9. So we divide both sides by -9.
→ x = (-18) ÷ (-9)
→ x = 2
✔ Check: -9 × 2 = -18 → Correct!
---
2) (5/6) + q = 1 1/3
First, convert mixed number to improper fraction:
1 1/3 = 4/3
So:
(5/6) + q = 4/3
Subtract 5/6 from both sides:
q = 4/3 - 5/6
Find common denominator (6):
4/3 = 8/6
So:
q = 8/6 - 5/6 = 3/6 = 1/2
✔ Check: 5/6 + 1/2 = 5/6 + 3/6 = 8/6 = 4/3 = 1 1/3 → Correct!
---
3) (7/9)t = -6
t is multiplied by 7/9. To undo that, multiply both sides by the reciprocal: 9/7.
t = -6 × (9/7) = -54/7
That’s an improper fraction. We can leave it like this or write as mixed number: -7 5/7
But since the problem doesn’t specify, we’ll keep it as -54/7.
✔ Check: (7/9) × (-54/7) = -54/9 = -6 → Correct!
---
4) t / 10 = -3
t is divided by 10. Multiply both sides by 10.
t = -3 × 10 = -30
✔ Check: -30 ÷ 10 = -3 → Correct!
---
5) -0.7 + s = 6.2
Add 0.7 to both sides to isolate s.
s = 6.2 + 0.7 = 6.9
✔ Check: -0.7 + 6.9 = 6.2 → Correct!
---
6) (2/3)z = -18
Multiply both sides by reciprocal of 2/3 → which is 3/2.
z = -18 × (3/2) = -54/2 = -27
✔ Check: (2/3) × (-27) = -54/3 = -18 → Correct!
---
7) a - 3.5 = -99
Add 3.5 to both sides.
a = -99 + 3.5 = -95.5
✔ Check: -95.5 - 3.5 = -99 → Correct!
---
8) y / (2/5) = 4/5
Dividing by a fraction? That’s same as multiplying by its reciprocal.
So: y × (5/2) = 4/5
Now multiply both sides by 2/5 to isolate y.
y = (4/5) × (2/5) = 8/25
Wait — let me double-check.
Actually, if y ÷ (2/5) = 4/5, then:
y = (4/5) × (2/5)? No — that’s wrong.
Correct way:
If y ÷ (2/5) = 4/5, then y = (4/5) × (2/5)? NO!
Division by fraction:
y ÷ (2/5) = y × (5/2)
So: y × (5/2) = 4/5
Then multiply both sides by 2/5:
y = (4/5) × (2/5) = 8/25? Wait — no:
To isolate y, multiply both sides by 2/5:
y = (4/5) × (2/5)? Let's think again.
Equation:
y × (5/2) = 4/5
Multiply both sides by 2/5:
y = (4/5) × (2/5) = 8/25? But that would be if we multiplied by 2/5 on right side.
Wait — actually:
Left side: [y × (5/2)] × (2/5) = y × (5/2 × 2/5) = y × 1 = y
Right side: (4/5) × (2/5) = 8/25
So yes, y = 8/25
✔ Check: (8/25) ÷ (2/5) = (8/25) × (5/2) = 40/50 = 4/5 → Correct!
---
9) -4 = g / (8/3)
Same idea: g divided by 8/3 equals -4.
So: g = -4 × (8/3) = -32/3
Or as mixed number: -10 2/3
✔ Check: (-32/3) ÷ (8/3) = (-32/3) × (3/8) = -96/24 = -4 → Correct!
---
10) 6.1b = 2.44
Divide both sides by 6.1.
b = 2.44 ÷ 6.1
Let’s calculate:
2.44 ÷ 6.1 = ?
Multiply numerator and denominator by 100 to eliminate decimals:
244 ÷ 610
Simplify: divide numerator and denominator by 2 → 122 / 305
Check if divisible further? 122 ÷ 2 = 61, 305 ÷ 5 = 61 → wait:
Actually, 2.44 ÷ 6.1 = 0.4
Because 6.1 × 0.4 = 2.44
Yes!
✔ Check: 6.1 × 0.4 = 2.44 → Correct!
---
Final Answer:
1) x = 2
2) q = 1/2
3) t = -54/7
4) t = -30
5) s = 6.9
6) z = -27
7) a = -95.5
8) y = 8/25
9) g = -32/3
10) b = 0.4
Parent Tip: Review the logic above to help your child master the concept of solving equations using inverse operation worksheet.
