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Linear Equations What They Are & How to Solve Them Definitions Equation – A mathematical sentence stating that 2 expressions are equal. 12 – 3 = 9x 8 + 4 = 12 6x – 12 = 42 Definitions Equals Sign (=) Means that the amount is the same on both sides. 4 +2=6 5 – 2 = 3 Definitions Linear Equation – An equation of the form: ax + b = c 14x + 3 = 17 An Equation is like a balance scale. Everything must be equal on both sides. = 10 5+5 When the amounts are equal on both sides it is a True Equation or Identity. = 12 6+6 When the amounts are unequal on both sides it is a False Equation or Contradiction. = 8 2+2 When an amount is unknown on one side of the equation it is an Open or Conditional Equation. = 7 n+2 When you find a number for n you change the open equation to a true equation. You solve the equation. = 7 5n + 2 Are these equations true, false or open? 11 -3=5 false true 13 + 4 = 17 open N + 4 = 7 false 12 – 3 = 8 3 + v = 13 open 15 – 6 = 9 true Definitions Inverse operation – the opposite operation used to undo the first. 4 +3=7 6 x 6 = 36 7–4=3 36 / 6 = 6 How to solve an addition equation Use the inverse operation for addition, which is subtraction. m + 8 = 12 8 is added to m - 8 -8 Subtract 8 on both sides m=4 How to solve a subtraction equation Use the inverse operation for subtraction, which is addition. m - 3 = 5 3 is subtracted from m +3 +3 Add 3 to both sides m=8 Solve these equations using the inverse operations n +4=7 n – 5 = 4 n + 4 = 17 n – 6 = 13 n + 7 = 15 n – 8 = 17 3 9 13 19 8 25 How to solve a multiplication equation Use the inverse operation for multiplication, which is division. 6m = 12 m is multiplied by 6 ______ _____ 6 6 Divide by 6 on both sides m = 2 How to solve a division equation Use the inverse operation for division, which is multiplication. m/3 = 4 m is divided by 3 3*(m/3) = 3*4 Multiply by 3, both sides m = 12 Solve these equations using the inverse operations 6 3n = 18 20 n/5 = 4 4 4n = 16 n/6 = 15 90 7n = 35 5 n/8 = 7 56 To solve equations Use the opposite operation variable alone Do the same thing to both sides to get the to keep the balance Bottom line: X = a number