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One, No, or Infinitely Many Solutions — Easy Worksheet 2
Grade 8 · MathSheets Name: ____________________ Date: __________
Write "one solution", "no solution", or "infinitely many solutions" for each equation.
How to solve
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Example
-2x + 1 = -11 + 4x
Answer: one solution
Not quite. The answer is
💡 The left side, −x + 5, is already simplified. Write the right side with the x-term first: 5 − x = −x + 5. Now the equation is −x + 5 = −x + 5. Both sides are exactly the same, so every value of x works: infinitely many solutions.
✓ Correct!
Not quite. The answer is
💡 The left side, −x + 5, is already simplified. Write the right side with the x-term first: 5 − x = −x + 5. Now the equation is −x + 5 = −x + 5. Both sides are exactly the same, so every value of x works: infinitely many solutions.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
5x - 1 = -3 + 4x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The left side, x + 8, is already simplified. Write the right side with the x-term first: −9 + 5x = 5x − 9. Now the equation is x + 8 = 5x − 9. The x-coefficients 1 and 5 are different, so exactly one value of x makes the two sides equal: one solution.
✓ Correct!
Not quite. The answer is
💡 The left side, x + 8, is already simplified. Write the right side with the x-term first: −9 + 5x = 5x − 9. Now the equation is x + 8 = 5x − 9. The x-coefficients 1 and 5 are different, so exactly one value of x makes the two sides equal: one solution.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
4x + 6 = 6 + 4x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The left side, −2x + 3, is already simplified. Write the right side with the x-term first: 8 − 2x = −2x + 8. Now the equation is −2x + 3 = −2x + 8. Both sides have −2x, but the numbers differ. Taking −2x away from both sides leaves 3 = 8, which is never true: no solution.
✓ Correct!
Not quite. The answer is
💡 The left side, −2x + 3, is already simplified. Write the right side with the x-term first: 8 − 2x = −2x + 8. Now the equation is −2x + 3 = −2x + 8. Both sides have −2x, but the numbers differ. Taking −2x away from both sides leaves 3 = 8, which is never true: no solution.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
-3x - 6 = 12 + x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The left side, −5x − 5, is already simplified. Write the right side with the x-term first: −5 − 5x = −5x − 5. Now the equation is −5x − 5 = −5x − 5. Both sides are exactly the same, so every value of x works: infinitely many solutions.
✓ Correct!
Not quite. The answer is
💡 The left side, −5x − 5, is already simplified. Write the right side with the x-term first: −5 − 5x = −5x − 5. Now the equation is −5x − 5 = −5x − 5. Both sides are exactly the same, so every value of x works: infinitely many solutions.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
5x - 10 = -10 + 5x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The left side, 3x − 8, is already simplified. Write the right side with the x-term first: −7 + 3x = 3x − 7. Now the equation is 3x − 8 = 3x − 7. Both sides have 3x, but the numbers differ. Taking 3x away from both sides leaves −8 = −7, which is never true: no solution.
✓ Correct!
Not quite. The answer is
💡 The left side, 3x − 8, is already simplified. Write the right side with the x-term first: −7 + 3x = 3x − 7. Now the equation is 3x − 8 = 3x − 7. Both sides have 3x, but the numbers differ. Taking 3x away from both sides leaves −8 = −7, which is never true: no solution.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
-4x + 8 = 8 - 4x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The left side, 4x − 8, is already simplified. Write the right side with the x-term first: −3 + 5x = 5x − 3. Now the equation is 4x − 8 = 5x − 3. The x-coefficients 4 and 5 are different, so exactly one value of x makes the two sides equal: one solution.
✓ Correct!
Not quite. The answer is
💡 The left side, 4x − 8, is already simplified. Write the right side with the x-term first: −3 + 5x = 5x − 3. Now the equation is 4x − 8 = 5x − 3. The x-coefficients 4 and 5 are different, so exactly one value of x makes the two sides equal: one solution.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
-x - 6 = -6 - x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The left side, −3x + 7, is already simplified. Write the right side with the x-term first: −6 − 2x = −2x − 6. Now the equation is −3x + 7 = −2x − 6. The x-coefficients −3 and −2 are different, so exactly one value of x makes the two sides equal: one solution.
✓ Correct!
Not quite. The answer is
💡 The left side, −3x + 7, is already simplified. Write the right side with the x-term first: −6 − 2x = −2x − 6. Now the equation is −3x + 7 = −2x − 6. The x-coefficients −3 and −2 are different, so exactly one value of x makes the two sides equal: one solution.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
-5x - 10 = -10 - 5x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The left side, 3x − 7, is already simplified. Write the right side with the x-term first: −7 + 3x = 3x − 7. Now the equation is 3x − 7 = 3x − 7. Both sides are exactly the same, so every value of x works: infinitely many solutions.
✓ Correct!
Not quite. The answer is
💡 The left side, 3x − 7, is already simplified. Write the right side with the x-term first: −7 + 3x = 3x − 7. Now the equation is 3x − 7 = 3x − 7. Both sides are exactly the same, so every value of x works: infinitely many solutions.
💡 How to solve: One, No, or Infinitely Many Solutions
Simplify both sides to the form ax + b. If the x-coefficients are different, there is one solution. If the x-coefficients match but the constants differ (like 7 = 3), there is no solution. If both sides are exactly the same, every x works: infinitely many solutions.
Try a similar one
5x - 8 = -3 + 5x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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One, No, or Infinitely Many Solutions — Easy Worksheet 2
Write "one solution", "no solution", or "infinitely many solutions" for each equation.