Algebra Tutorials! Home Solving Quadratic Equations by Completing the Square Graphing Logarithmic Functions Division Property of Exponents Adding and Subtracting Rational Expressions With Like Denominators Rationalizing the Denominator Multiplying Special Polynomials Functions Solving Linear Systems of Equations by Elimination Solving Systems of Equation by Substitution and Elimination Polynomial Equations Solving Linear Systems of Equations by Graphing Quadratic Functions Solving Proportions Parallel and Perpendicular Lines Simplifying Square Roots Simplifying Fractions Adding and Subtracting Fractions Adding and Subtracting Fractions Solving Linear Equations Inequalities in one Variable Recognizing Polynomial Equations from their Graphs Scientific Notation Factoring a Sum or Difference of Two Cubes Solving Nonlinear Equations by Substitution Solving Systems of Linear Inequalities Arithmetics with Decimals Finding the Equation of an Inverse Function Plotting Points in the Coordinate Plane The Product of the Roots of a Quadratic Powers Solving Quadratic Equations by Completing the Square
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# Solving Linear Equations

## Strategy for Solving Linear Equations

The most basic equations of algebra are linear equations. There is even a connection between linear equations in one variable and straight lines.

Linear Equation in One Variable

A linear equation in one variable x is an equation of the form ax + b = 0, where a and b are real numbers, with a ≠ 0.

A linear equation has exactly one solution. The strategy that we use for solving linear equations is summarized in the following lines.

Strategy for Solving a Linear Equation

1. If fractions are present, multiply each side by the LCD to eliminate them.

2. Use the distributive property to remove parentheses.

3. Combine any like terms.

4. Use the addition property of equality to get all variables on one side and numbers on the other side.

5. Use the multiplication property of equality to get a single variable on one side.

6. Check by replacing the variable in the original equation with your solution.

Note that not all equations require all of the steps.

Example 1

Using the equation-solving strategy

Solve the equation Solution

We first multiply each side of the equation by 10, the LCD for 2, 5, and 10. However, we do not have to write down that step. We can simply use the distributive property to multiply each term of the equation by 10.    Multiply each side by 10. 5y - 2(y - 4) = 23 Divide each denominator into 10 to eliminate fractions. 5y - 2y + 8 = 23 Be careful to change all signs: -2(y - 4) = -2y + 8 3y + 8 = 23 Combine like terms. 3y + 8 - 8 = 23 - 8 Subtract 8 from each side. 3y = 15 Simplify  Divide each side by 3. y = 5

Check that 5 satisfies the original equation. The solution set is {5}.