Unit 15 COMPLEX EQUATIONS.

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Presentation transcript:

Unit 15 COMPLEX EQUATIONS

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

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

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

EQUATIONS CONSISTING OF COMBINED OPERATIONS Solve for p: Multiply both sides by 40 p2 = 3600 Square root both sides p = 60 Ans

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 = 33.51 in3 Ans

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.

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

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.

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

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.

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

PROBLEM ANSWER KEY 2 –28 27 –7 6 197.92 cm3 22.22º