Section 2.2 Solving Linear Equations 135 2 7x 5 61x 32 2x Step 4: Because the coefficient of the x term is already 1, there is no need to apply the multiplication or division property of equality. Classroom Example: p. 138, Exercise 50 10 1x 52 3x Answers 6. 7. 3 7 4 Solving a Linear Equation Example 6 Solve the equation. Solution: Step 1: Add like terms on the left. Clear parentheses on the right. Combine like terms. Step 2: Subtract 7x from both sides. Simplify. Step 3: Subtract 18 from both sides. 2 7x 5 61x 32 2x 3 7x 6x 18 2x 3 7x 8x 18 3 7x 7x 8x 7x 18 3 x 18 3 18 x 18 18 21 x x 21 The solution is 21. Step 5: The check is left to the reader. Skill Practice Solve the equation. 6. 412y12y 6y3y Skill Practice Solve the equation. 7. 6x 51x 12 3 Solving a Linear Equation Solve the equation. Solution: 9 1z 32 4z 4z 51z 22 6 Step 1: Clear parentheses. Combine like terms. Step 2: Add z to both sides. Step 4: Divide both sides by 4. Step 5: The check is left for the reader. 9 1z 32 4z 4z 51z 22 6 9 z 3 4z 4z 5z 10 6 12 3z z 16 12 3z z z z 16 12 4z 16 12 12 4z 16 12 The solution is 7. 4z 28 4z 4 z 7 28 4 Example 7 Step 3: Subtract 12 from both sides. 3. Conditional Equations, Identities, and Contradictions The solutions to a linear equation are the values of x that make the equation a true statement. A linear equation in one variable has one unique solution. Some types of equations, however, have no solution while others have infinitely many solutions. Classroom Example: p. 138, Exercise 54 Avoiding Mistakes When distributing a negative number through parentheses, be sure to change the signs of every term within parentheses.
miller_introductory_algebra_3e_ch1_3
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