1. Unit 15
COMPLEX EQUATIONS

2. SOLVING EQUATIONS Remove parentheses
Combine like terms on each side of equation
Get all unknown terms on one side and all known terms on the other using addition and subtraction principle
Combine like terms
Apply multiplication and division principles of equality
Apply power and root principles of quality

3. EQUATIONS CONSISTING OF COMBINED OPERATIONS
Complex equations require the use of two or more principles of equality for their solutions
Solve for x: 7x + 4 = 39
x = 5 Ans

4. EQUATIONS CONSISTING OF COMBINED OPERATIONS
Solve for y: 5y – 3(2y – 6) = 12
5y – 3(2y – 6) = 12
5y – 6y = Remove parentheses
–1y = Combine like terms
– 18 – Subtract 18 from both sides
y = –12 Ans

5. EQUATIONS CONSISTING OF COMBINED OPERATIONS
Solve for p:
Multiply both sides by 40
p2 = Square root both sides
p = 60 Ans

6. SUBSTITUTING INTO FORMULAS
The volume of a sphere is given as 4/3 times  times the radius cubed. Set up the formula and determine the volume given that the radius is 2 inches
Set up the formula:
Substitute 2 inches for r:
Solve for the volume:
V = in3 Ans

7. REARRANGING FORMULAS
Sometimes it is necessary to rearrange a formula to solve for another value.
The formula must be rearranged so that the unknown term is on one side of the equation and all other values are on the other side.
The formula is rearranged by using the same procedure that is used for solving equations consisting of combined operations.

8. REARRANGING FORMULAS Rearrange the formula A = 1/2bh to solve for b:
Multiply both sides by 2
Divide both sides by h

9. REARRANGING FORMULAS Rearrange P = I2R to solve for I:
Divide both sides by R
Square root both sides
Whenever taking a square root there are two solutions that are usually denoted by ± and should be in front of all roots but then are determined viable or not.

10. PRACTICE PROBLEMS
7x – 3 = 11
15 – (y – 7) = 50

11. PRACTICE PROBLEMS (Cont)
y(3 + y) + 14 = y2 – 7
x3 – 3x = 3(72 – x)
Given that the volume of a right circular cylinder is  times radius squared times height. Determine the volume given that the radius is three centimeters and the height is seven centimeters.

12. PRACTICE PROBLEMS (Cont)
Find the Celsius temperature using the formula C = 5/9(F – 32º) when the Fahrenheit temperature is 72 degrees

13. PROBLEM ANSWER KEY 2
–28 27 –7 6
cm3
22.22º