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MATH 0960 K. Rigdon STEPS TO SOLVE Linear Equations 1) If the equation contains fractions or decimals, multiply both sides of the equation to clear them (clearing the fractions & decimals is optional, but recommended)… To clear the decimals - Multiply by the largest place value name (without the “th”) to clear the fractions - Multiply by the Least Common Denominator (LCD) REMEMBER: multiply every term, not just the term(s) with the decimals or fractions, but the whole numbers and/or the terms with just the variable as well…. Also remember: whatever is in parentheses in this step is protected from this multiplication (if further fractions or decimals are inside the parentheses, you will either need to do step 2 first, or do step 1 a second time, after you have done step 2) 2) If the equation contains PARENTHESES, use the DISTRIBUTIVE PROPERTY to clear them 3) Combine LIKE TERMS on the SAME SIDE of the equal sign 4) Use the ADDITION PROPERTY to rewrite the equation so that all the TERMs with the VARIABLE are ISOLATED on ONE SIDE of the equation (can also subtract, remember) – may have to use the property twice (once on term with variable and once on constant term) IF THE TERMS WITH THE VARIABLES CANCEL OUT COMPLETELY, YOU WILL HAVE ONE OF TWO SPECIAL SITUATIONS… If the numbers that are left are really equal, then it means any number you can think of will make the equation true x = all real numbers (or ) called IDENTITY If the numbers that are left are not equal, then it means that there is no number that will make the equation true x = the empty set (no solution or 0 ) called CONTRADICTION 5) Use the MULTIPLICATION PROPERTY to SOLVE for the variable (can also divide, remember) 6) CHECK your solution in the original equation.