Wake Forest University Department of Economics Kosmas Marinakis, Ph.D. Handout 4 – Solving Linear Equations A linear equation is an expression of the form: ax + b = c For example the expression: 5x + 2 = 12 is a linear equation. Every linear equation contains one unknown (or variable), usually called x. By solving the equation we can find out what is the value of the unknown which satisfies the equality. In order to solve for the value of x we have to follow some certain steps. Steps for Solving Linear Equations 1. Remove any parentheses and combine like terms, if possible, on each side of the equation. 2. Clear any fractions by multiplying all terms on both sides by the least common denominator. 3. Group like terms on each side of the equal sign. 4. Isolate the "x term" (variable) on one side of the equation by adding or subtracting to combine like terms across the equal sign. 5. Divide or multiply both sides of the equation by the coefficient of the variable to solve for "x". Note that some steps might not be necessary for every equation. We can check the solution by substituting your answer into the original equation wherever we have a variable. If the solution is correct, both sides of the equation will be equal. Example Solve the equation: Step 1: 0.5(5x + 2) = 12/2 (1) Multiply both terms of the parenthesis with 0.5 to eliminate the parenthesis. Equation becomes 2.5x + 1 = 12/2 Step 2: Multiply both sides by 2 to eliminate the fraction of the Right Hand Side (RHS). Equation becomes: 5x + 2 = 12 Step 3: There are no like terms in each side. Go to step 4. Step 4: We subtract from both sides 2 to eliminate the 2 in the LHS. Equation becomes: 5x = 10 Step 5: We divide both sides by 5 to cancel the 5 from the LHS. Therefore, x = 2 Now try to put 2 instead of x in (1) and check if the two sides are equal.