# Solutions of a Linear Equation

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Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades

Examples, videos, and solutions to help Grade 8 students learn how to solve equations that are not obviously linear equations.

### New York State Common Core Math Grade 8, Module 4, Lesson 6

Common Core Math Grade 8, Module 6, Lesson 4 Worksheets (pdf)

### Lesson 6 Outcome

• Students transform equations into simpler forms using the distributive property.
• Students learn that not every linear equation has a solution.

### Lesson 6 Summary

• The distributive property is used to expand expressions. For example, the expression 2(3x - 10) is rewritten as 6x - 20 after the distributive property is applied.

• The distributive property is used to simply expressions. For example, the expression 7x + 11x is rewritten as (7 + 11)x and 18x after the distributive property is applied.

• The distributive property is applied only to terms within a group:
4(3x + 5) - 2 = 12x + 20 - 2
Notice that the term -2 is not part of the group and therefore not multiplied by 4

• When an equation is transformed into an untrue sentence, like 5 ≠ 11, we say the equation has no solution.

### NYS Math Module 4 Grade 8 Lesson 6 Examples

Example 1:
What value of would make the linear equation 4x + 3(4x + 7) = 4(7x + 3) - 3 true? What is the “best” first step and why?

Example 2: What value of would make the following linear equation true: 20 - (3x - 9) - 2 = -(-11x + 1)?

Example 3: What value of would make the following linear equation true: ½ (4x + 6) - 2 = -(5x + 9). Begin by transforming both sides of the equation into a simpler form.

Example 4: Consider the following equation: 2(x + 1) = 2x - 3. What value of makes the equation true?

Example 5 : So far we have used the distributive property to simplify expressions when solving equations. In some cases, we can use the distributive property to make our work even simpler.

Exercises
Find the value of that makes the equation true.
1. 17 - 5(2x -9) = -(-6x +10) + 4
2. -(x - 7) + 5/3 = 2(x + 9)
3. 4/9 + 4(x - 1) = 28/9 - (x - 7x) + 1
4. 5(3x + 4) - 2x = 7x - 3(2x -11)
5. 7x - (3x + 5) - 8 = 1/2(8x + 20) - 7x + 5
6. Write at least three equations that have no solution.
Example 1 - Example 4

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