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

Examples, videos, and solutions to help Grade 8 students learn that a linear equation is a statement of equality between two expressions.

### New York State Common Core Math Module 4, Grade 8, Lesson 3

### Lesson 3 Student Outcomes

Exercises 1–6

1. Is the equation true when x = -3; in other words, is -3 a solution to the equation: 6x + 5 = 5x + 8 + 2x? Explain.

2. Does x = 12 satisfy the equation: 16 - 1/2 x = 3/4 x + 1? Explain.

3. Chad solved the equation 24x + 4 + 2x = 3(10x - 1) and is claiming that x = 2 makes the equation true. Is Chad correct? Explain.

4. Lisa solved the equation x + 6 = 8 + 7x and claimed that the solution is x = -1/3. Is she correct? Explain.

5. Angel transformed the following equation from 6x + 4 - x = 2(x + 1) to 10 = 2(x + 1). He then stated that the solution to the equation is x = 4. Is he correct? Explain.

6. Claire was able to verify that x = 3 was a solution to her teacher’s linear equation, but the equation got erased from the board. What might the equation have been? Identify as many equations as you can with a solution of x = 3.

7. Does an equation always have a solution? Could you come up with an equation that does not have a solution?

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.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn that a linear equation is a statement of equality between two expressions.

• Students know that a linear equation is a statement of equality between two expressions.

• Students know that a linear equation in x is actually a question: Can you find all numbers x, if they exist, that
satisfy a given equation? Students know that those numbers x that satisfy a given equation are called
solutions.

Lesson 3 Summary

Equations are statements about equality. If the expression on the left side of the equal sign has the same value as
the expression on the right side of the equal sign, then you have a true equation.

A solution to a linear equation in is a number, such that when all instances of are replaced with the number, the
left side will equal the right side.

Classwork

Example 1

Here is a linear equation in x: 4 + 15x = 49. The question is, is there a number x
that makes the linear expression 4 + 15x equal to the linear expression 49?

Example 2

Here is a linear equation in x: 8x - 19 = -4 - 7x

Is 5 a solution to the equation?

Is 1 a solution to the equation?

Example 3

Here is a linear equation in x: 3(x + 9) = 4x - 7 + 7x.

Example 4

Here is a linear equation in x: -2x + 11 - 5x = 5 - 6x

1. Is the equation true when x = -3; in other words, is -3 a solution to the equation: 6x + 5 = 5x + 8 + 2x? Explain.

2. Does x = 12 satisfy the equation: 16 - 1/2 x = 3/4 x + 1? Explain.

3. Chad solved the equation 24x + 4 + 2x = 3(10x - 1) and is claiming that x = 2 makes the equation true. Is Chad correct? Explain.

4. Lisa solved the equation x + 6 = 8 + 7x and claimed that the solution is x = -1/3. Is she correct? Explain.

5. Angel transformed the following equation from 6x + 4 - x = 2(x + 1) to 10 = 2(x + 1). He then stated that the solution to the equation is x = 4. Is he correct? Explain.

6. Claire was able to verify that x = 3 was a solution to her teacher’s linear equation, but the equation got erased from the board. What might the equation have been? Identify as many equations as you can with a solution of x = 3.

7. Does an equation always have a solution? Could you come up with an equation that does not have a solution?

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.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.