114 Chapter 2 Linear Equations and Inequalities TIP: It is important to note that the variable may be isolated on either side of the equation. We will solve the equation from Example 3 again, this time isolating the variable on the right-hand side. 6x 4 2x 8 6x 6x 4 2x 6x 8 0x 4 4x 8 4 4x 8 4 8 4x 8 8 4 4x 4 4 4x 4 2. Procedure for Solving a Linear Equation in One Variable In some cases, it is necessary to simplify both sides of a linear equation before applying the properties of equality.Therefore, we offer the following steps to solve a linear equation in one variable. Solving a Linear Equation in One Variable Step 1 Simplify both sides of the equation. • Clear parentheses • Combine like terms Step 2 Use the addition or subtraction property of equality to collect the variable terms on one side of the equation. Step 3 Use the addition or subtraction property of equality to collect the constant terms on the other side of the equation. Step 4 Use the multiplication or division property of equality to make the coefficient of the variable term equal to 1. Step 5 Check your answer. Solving a Linear Equation Solve the equation. Solution: Step 1: Simplify both sides of the equation by clearing parentheses and combining like terms. Step 2: The variable terms are already on one side. Step 3: Add 6 to both sides to collect the constant terms on the other side. 7 3 2 1 p 32 10 2p 6 10 6 2p 6 6 16 2p 7 3 21 p 32 Example 4 Subtract 6x on both sides. Add 8 to both sides. Divide both sides by 4. 1 x or equivalently x 1
miller_beginning_intermediate_algebra_4e_ch1_3
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