1. Unit 14
SIMPLE EQUATIONS

2. 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

3. 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

4. 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 = 12
– – 7
x = Ans

5. 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

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

7. 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

8. 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

9. 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

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

11. 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

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

13. 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

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

15. 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 = 16.3
x – 4/5 = 2/3
5.4y = 18.9

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

17. PROBLEM ANSWER KEY 1. 4x – 12 = 36 2. (2x – 6) + 3x = 14 3. 15
/15
10. 7/15