It looks like you've uploaded an image of a
completed math worksheet titled
"Two Step Equations - Integers", with the
answer key already filled in. This is a
Math Worksheet 11 from
DadsWorksheets.com, and it contains
12 two-step equations involving integers.
Since the
answers are already provided, I'll go through
one example problem in detail to explain how to solve such equations step-by-step, then summarize the general method.
---
🔍 Example Problem (Top Left):
>
84 / (n - 92) + 150 = 156
#### Step 1: Isolate the fraction
Subtract 150 from both sides:
$$
\frac{84}{n - 92} + 150 - 150 = 156 - 150
$$
$$
\frac{84}{n - 92} = 6
$$
#### Step 2: Eliminate the denominator
Multiply both sides by $ n - 92 $:
$$
84 = 6(n - 92)
$$
#### Step 3: Distribute
$$
84 = 6n - 552
$$
#### Step 4: Solve for $ n $
Add 552 to both sides:
$$
84 + 552 = 6n \Rightarrow 636 = 6n
$$
Divide by 6:
$$
n = 106
$$
✔ Check: Plug back into original equation:
$$
\frac{84}{106 - 92} + 150 = \frac{84}{14} + 150 = 6 + 150 = 156 \quad \text{✓ Correct}
$$
---
✔ General Strategy for Two-Step Equations:
For equations like:
$$
\frac{a}{x - b} + c = d
$$
or
$$
\frac{a}{x} + b = c
$$
Follow these steps:
1.
Isolate the term with the variable (usually the fraction).
2.
Eliminate the denominator by multiplying both sides.
3.
Solve the resulting linear equation using inverse operations.
4.
Check your solution by plugging it back into the original equation.
---
🧠 Tips for Solving These Types of Problems:
- Always
check for division by zero — make sure the denominator is not zero in the original equation.
- Use
inverse operations:
- Addition → Subtraction
- Multiplication → Division
- Work step-by-step and show all work (as instructed).
- Simplify fractions when possible.
---
📌 Summary of All Answers (from Answer Key):
| Equation | Solution |
|--------|---------|
| 1. $ \frac{84}{n-92} + 150 = 156 $ | $ n = 106 $ |
| 2. $ \frac{x+39}{107} + 80 = 66 $ | $ x = -1,537 $ |
| 3. $ \frac{68}{y+50} + 53 = 45 $ | $ y = -47 $ |
| 4. $ 97 - \frac{s-81}{55} = 46 $ | $ s = 2886 $ |
| 5. $ 74 = \frac{a-52}{61} + 68 $ | $ a = 418 $ |
| 6. $ 49 + \frac{m-39}{78} = 93 $ | $ m = 3471 $ |
| 7. $ \frac{d+27}{116} - 53 = 48 $ | $ d = 11,689 $ |
| 8. $ 16 = \frac{180}{p-90} - 44 $ | $ p = 93 $ |
| 9. $ 82 + \frac{w+46}{97} = 81 $ | $ w = -143 $ |
| 10. $ 71 - \frac{z-76}{128} = 69 $ | $ z = 332 $ |
| 11. $ 95 = \frac{a-122}{68} + 143 $ | $ a = -3142 $ |
| 12. $ \frac{174}{n+82} + 56 = 62 $ | $ n = -5 $ |
---
✔ Final Notes:
- The worksheet is designed for
practice in solving two-step equations with integers.
- It includes
fractions, variables in denominators, and negative numbers.
- The answer key shows
correct algebraic manipulation.
- If you're learning, focus on
understanding each step, not just copying answers.
Let me know if you'd like help solving any specific problem or want a printable version!
Parent Tip: Review the logic above to help your child master the concept of integer equations worksheet.
