Solving a Linear Equation

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Common Core For Grade 8

Examples, worksheets, videos, and solutions to help Grade 8 students extend the use of the properties of equality to solve linear equations having rational coefficients.

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

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

Lesson 4 Summary:

The properties of equality, shown below, are used to transform equations into simpler forms. If A, B and C are rational numbers, then

If A = B, then A + C = B + C (Addition Property of Equality)

If A = B, then A - C = B - C (Subtraction Property of Equality)

If A = B, then A•C = B•C (Multiplication Property of Equality)

If A = B, then A/C = B/C, where is not equal to zero (Division Property of Equality)

To solve an equation, transform the equation until you get to the form of x equal to a constant (x = 5, for example).

Lesson 4 Concept Development

To solve an equation means to find all of the numbers , if they exist, so that the given equation is true.

Example 1 - Example 3

Exercises 1ֵ
For each problem, show your work and check that your solution is correct.
1. Solve the linear equation: x + x + 2 + x + 4 + x + 6 = -28. State the property that justifies your first step and why you chose it.

2. Solve the linear equation: 2(3x + 2) = 2x - 1 + x. State the property that justifies your first step and why you chose it.

3. Solve the linear equation: x - 9 = 3/5 x. State the property that justifies your first step and why you chose it.

4. Solve the linear equation: 29 - 3x = 5x + 5. State the property that justifies your first step and why you chose it.

5. Solve the linear equation: 1/3 x - 5 + 171 = x. State the property that justifies your first step and why you chose it.

Lesson 4 Concept Development

Example 1:
Solve the linear equation 2x - 3 = 4x for the number x.

Example 2:
Solve the linear equation 3/5 x - 21 = 15

Example 3:
Solve the linear equation 1/5 x + 13 + x = 1 - 9x + 22. State the property that justifies your first step and why you chose it.

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