Section 1.1 Linear Equations in One Variable 47 For more complicated linear equations, several steps are required to isolate the variable.These steps are listed below. Solving a Linear Equation in One Variable Step 1 Simplify both sides of the equation. • Clear parentheses. • Consider clearing fractions or decimals (if any are present) by multiplying both sides of the equation by a common denominator of all terms. • 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 and write the solution set. Solving a Linear Equation Example 3 Solve the linear equation and check the answer. Solution: 3x 1 7 Subtract 1 from both sides. Combine like terms. To isolate x, divide both sides of the equation by 3. Simplify. Check: ✓ True. 3x 1 7 3x 1 1 7 1 3x 8 3x 3 8 3 x The solution set is 8 3 e 8 3 f . 3a 3a 3x 1 7 8 3 8 3 b 1 7 b 1 7 8 1 7 7 7 Skill Practice Solve the linear equation and check the answer. 5. 5x 19 23 Answer 5. e 4 5 f
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