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Linear Equations in x

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Lesson Plans and Worksheets for Grade 8
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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

• 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.

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

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?

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