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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.

Try the free Mathway calculator and problem solver below to practice various 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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