Solving Linear Equations

Objectives

  • Solve linear equations in one variable (Section R2.3 objectives 1, 2, and 4).

  • Identify conditional equations, identities, and contradictions.

Steps to Solve a Linear Equation in One Variable

  • Step 1: Simplify both sides of the equation.

    • Use the distributive property to clear parentheses.

    • Combine like terms.

    • Consider clearing fractions or decimals by multiplying both sides of the equation by the least common denominator (LCD\text{LCD}) of all terms.

  • Step 2: Use the addition property of equality to collect the variable terms on one side of the equation and the constant terms on the other side.

  • Step 3: Use the multiplication property of equality to make the coefficient on the variable term equal to 11.

  • Step 4: Check the potential solution in the original equation.

  • Step 5: Write the solution set.