Videos, examples, solutions to help Grade 8 students know the conditions for which a linear equation will have a unique solution, no solution, or infinitely many solutions.

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Common Core For Grade 8

### New York State Common Core Math Grade 8, Module 4, Lesson 7

### Lesson 7 Outcome

### Lesson 7 Summary

• There are three classifications of solutions to linear equations: one solution (unique solution), no solution, or
infinitely many solutions.

Equations with no solution will, after being simplified, have coefficients of x that are the same on both sides of the equal sign and constants that are different. For example, x + b = x + c, where b, c are constants that are not equal. A numeric example is 8x + 5 = 8x - 3.

Equations with infinitely many solutions will, after being simplified, have coefficients of x and constants that are the same on both sides of the equal sign. For example, x + a = x + a, where a is a constant. A numeric example is 6x + 1 = 1 + 6x.

### NYS Math Module 4 Grade 8 Lesson 7 Classwork

Exercises 1–3

Solve each of the following equations for x.

1. 7x - 3 = 5x + 5

2. 7x - 3 = 7x + 5

3. 7x - 3 = -3 + 7x

Note: if the coefficients of x are different and the value of the constants are the same, the only solution is x = 0. For example, 2x + 12 = x + 12 Exercises 1–3

Activity: What can we see in an equation that will tell us about the solution to the equation?

Exercises 4–10

Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary.

4. 11x - 2x + 15 = 8 + 7 + 9x

5. 3(x -14) + 1 = -4x + 5

6. -3x + 32 - 7x = -2(5x + 10)

7. 1/2(8x + 26) = 13 + 4x

8. Write two equations that have no solutions.

9. Write two equations that have one unique solution each.

10. Write two equations that have infinitely many solutions.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

• Students know the conditions for which a linear equation will have a unique solution, no solution, or infinitely many solutions.

Equations with no solution will, after being simplified, have coefficients of x that are the same on both sides of the equal sign and constants that are different. For example, x + b = x + c, where b, c are constants that are not equal. A numeric example is 8x + 5 = 8x - 3.

Equations with infinitely many solutions will, after being simplified, have coefficients of x and constants that are the same on both sides of the equal sign. For example, x + a = x + a, where a is a constant. A numeric example is 6x + 1 = 1 + 6x.

Solve each of the following equations for x.

1. 7x - 3 = 5x + 5

2. 7x - 3 = 7x + 5

3. 7x - 3 = -3 + 7x

Note: if the coefficients of x are different and the value of the constants are the same, the only solution is x = 0. For example, 2x + 12 = x + 12 Exercises 1–3

Activity: What can we see in an equation that will tell us about the solution to the equation?

Exercises 4–10

Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary.

4. 11x - 2x + 15 = 8 + 7 + 9x

5. 3(x -14) + 1 = -4x + 5

6. -3x + 32 - 7x = -2(5x + 10)

7. 1/2(8x + 26) = 13 + 4x

8. Write two equations that have no solutions.

9. Write two equations that have one unique solution each.

10. Write two equations that have infinitely many solutions.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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