Unit 14 SIMPLE EQUATIONS

WRITING EQUATIONS The following examples illustrate writing equations from given word statements A number less 15 equals 36: Let n = the number Three times a number plus 11 equals 20: Let x = the number Three times the number would then be 3x The equation would become: n – 15 = 36 Ans The equation is now: 3x + 11 = 20 Ans

SUBTRACTION PRINCIPLE OF EQUALITY The subtraction principle of equality states: If the same number is subtracted from both sides of an equation, the sides remain equal The equation remains balanced

SUBTRACTION PRINCIPLE OF EQUALITY Procedure for solving an equation in which a number is added to the unknown: Subtract the number that is added to the unknown from both sides of the equation Solve x + 7 = 12 for x: x + 7 = 12 – 7 – 7 x = 5 Ans

ADDITION PRINCIPLE OF EQUALITY Procedure for solving an equation in which a number is subtracted from the unknown. Add the number, which is subtracted from the unknown, to both sides of an equation The equation maintains its balance

ADDITION PRINCIPLE OF EQUALITY Solve for p: p – 19 = 42 +19 + 19 Solve for y: y – 43.5 = 6.79 + 43.5 + 43.5 p = 61 Ans y = 50.29 Ans

DIVISION PRINCIPLE OF EQUALITY Procedure for solving an equation in which the unknown is multiplied by a number: Divide both sides of the equation by the number that multiplies the unknown The equations maintains its balance

DIVISION PRINCIPLE OF EQUALITY (Cont) Solve for t: 9t = 18.9 Solve for x:-3.5x = 9.625 t = 2.1 Ans x = –2.75 Ans

MULTIPLICATION PRINCIPLE OF EQUALITY Procedure for solving an equation in which the unknown is divided by a number: Multiply both sides of the equation by the number that divides the unknown Equation maintains in balance

MULTIPLICATION PRINCIPLE OF EQUALITY (Cont) Solve for r: r = 16 Ans

ROOT PRINCIPLE OF EQUALITY Procedure for solving an equation in which the unknown is raised to a power: Extract the root of both sides of the equation that leaves the unknown with an exponent of 1 Equation maintains in balance

ROOT PRINCIPLE OF EQUALITY (Cont) Solve for R: R3 = 27 R = 3 Ans

POWER PRINCIPLE OF EQUALITY Procedure for solving an equation which contains a root of the unknown: Raise both sides of the equation to the power that leaves the unknown with an exponent of 1 Equation maintains in balance

POWER PRINCIPLE OF EQUALITY (Cont) Solve for x: x = 3125 Ans

PRACTICE PROBLEMS Express each of the following word problems as an equation: Four times a number minus 12 equals 36 Six subtracted from two times a number, plus three times the number, equals fourteen Solve each of the following equations: x + 7 = 22 n – 4.76 = 9.3 2/3m = 16 C  2.7 = 19.1 m + 9.1 = 16.3 x – 4/5 = 2/3 5.4y = 18.9

PRACTICE PROBLEMS p  4/5 = 7/12 121 = y2

PROBLEM ANSWER KEY 1. 4x – 12 = 36 2. (2x – 6) + 3x = 14 3. 15 3. 15 4. 14.06 5. 24 6. 51.57 7. 7.2 8. 1 7/15 9. 3.5 10. 7/15 11. 11