SIMPLE EQUATIONS

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UNIT 13

• SIMPLE EQUATIONS

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WRITING EQUATIONS

• It is important to develop the ability to express
  word statements as mathematical symbols, or
  equations
• The following examples illustrate writing
  equations from given word statementsa. A number
  less 15 equals 36
• Let n the number
• b. 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

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SUBTRACTION PRINCIPLE OF EQUALITY

• The subtraction principle of equality states that
  if the same number is subtracted from both sides
  of an equation, the sides remain equal and the
  equation remains balanced
• 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
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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
• 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
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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
• Solve for t
• Solve for x

t 2.1 Ans
x 2.75 Ans
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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
• Solve for r

r 16 Ans
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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
• Solve for R R3 27

R 3 Ans
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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
• Solve for x

x 3125 Ans
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PRACTICE PROBLEMS

• Express each of the following word problems as an
  equation
• 1. Four times a number minus 12 equals 36
• 2. Six subtracted from two times a number,
  plus three times the
• number, equals fourteen
• Solve each of the following equations
• 3. x 7 22
• 4. n 4.76 9.3
• 5. 2/3m 16
• 6. C ? 2.7 19.1
• 7. m 9.1 16.3
• 8. x 4/5 2/3
• 9. 5.4y 18.9

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PRACTICE PROBLEMS

• 10. p ? 4/5 7/12
• 11. 121 y2

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PROBLEM ANSWER KEY

• 1. 4x 12 36
• 2. (2x 6) 3x 14
• 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