Answers to Basic Algebra Review

Transcription

1 Answers to Basic Algebra Review Follow the sign rules when adding and subtracting: If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract the numbers and keep the sign of the larger number.. 9 Follow the Order of Operations at all times. You can remember the Order of Operations by the phrase Please Ecuse My Deal Aunt Sally. For a more detailed eplanation visit Parentheses Eponents Multiplication / Division starting at the left and moving to the right Addition Subtraction. 41 Order of Operations was used to evaluate the epression. (1 5) 8 ( 4) 8 (15) Do what is inside parentheses first and rewrite the problem. Net do the eponents and rewrite the problem. Net is multiplication, followed by addition and subtraction. For more eamples, visit of%0operations%0eamples.pdf

2 Follow the Order of Operations The problem states to translate the statement. It does not say to simplify. If it asked you to simplify, you would get 9 < > As negative numbers become larger, they are getting smaller Follow the sign rules for multiplying signed numbers. For more information, visit pdf y ( )() ( )(9) 4(9) ( 5)

3 9. 1 To get by itself, add the opposite of -11 to both sides V 11. h r These problems can be tricky. Since we want to get h by itself, we have to get everything away from it. We would need to divide both sides by r to get the h alone First we add the opposite of -5 to both sides to get the fraction and by itself. Then multiply both sides by the reciprocal of the fraction

4 1. ( 6) To learn more about solving linear equations, visit 8/16686.pdf ( 4) 0.5( ) To learn more about solving linear equations, visit 8/16686.pdf 15. $70 Original price 0% discount of original price = sale price = Joe = Jane = + 8 Equation:

5 or 1 For the number line you would have a closed circle about the 1 and an arrow pointing to the left. 18. y = y y= y y=

6 y y Slope m 11 ( 1) Perpendicular Compare the slope of each line. One is and the other is which is the reciprocal and opposite sign of the first one. If I multiply these two slopes together, I would get -1 which indicates that it is perpendicular.. y Use the point-slope formula to find the equation of the line. y y m( ) 1 1 y ( 9) ( 4) y 9 1 y Substitute - in for and evaluate. ( ) 7 (4)

7 ( ) means to multiply - by itself 7 times. Since the eponent is odd, the answer will remain negative To learn more about negative eponents, visit ve%0eponents.pdf 7. y 6 Follow the eponent rules. 8. 8y 18 9 Apply the outside eponent to all eponents (and the invisible 1 s) first: y y 6 1 Now change all negative eponents to positive eponents by following the rules and simplify. 8 y y 8y y y y Distribute and follow the eponent rules for multiplying.

8 Simplify following rules for like terms When a minus sign appears outside parentheses, you will change the sign to positive AND change the sign of everything in the following parentheses to its opposite sign and then combine like terms Use FOIL to multiply the two binomials together and then combine like terms.. 6y 1 Since you are dividing a polynomial by a monomial, break up the problem into separate fractions with the same denominator and reduce. 4. 5ab Look for the largest number each term has in common and the lowest eponent on the variables y ( 6y y) Factoring guidelines can be found at

9 Factoring is used etensively in algebra. 6. ( 9)( 9) This is a difference of squares. Follow the factoring guidelines. 7. ( 9)( ) Follow the factoring guidelines. 8. (5)( 5) This is a perfect square trinomial. Follow the factoring guidelines. 9. ()( 7) Follow the factoring guidelines for using the ac method. 40. ( 5)( 5) First factor out the greatest common factor and then follow the guidelines for factoring the difference of squares. 41. and 1 Factor the equation first and use the zero factor theorem to find the values for. A quadratic equation will have two answers Get the squared term by itself first and then take the square root of both sides.

10 4. 5 To find what makes a rational epression undefined, we set the denominator equal to zero and solve for the variable. An epression that is undefined means we are dividing by First factor both the numerator and the denominator and then reduce like terms. 6 ( ) 4 ( )( ) ( ) 45. 5( 4) Factor both of the rational epressions. Since we are dividing the rational epressions, we need to remember Keep, Change, Flip when dividing fractions. Keep the first one, change division to multiplication, and flip the epression that comes after the division sign. 7 1 ( )( 4) ( 5) Now rewrite the problem changing division to multiplication and flipping the following fraction. ( )( 4) 5( 5) 5 Now cancel out the like terms. 5( 4) Follow the rules for simplifying square roots found at:

11 47. 5 Follow the rules for simplifying square roots Follow the rules for simplifying square roots y Follow the rules for simplifying square roots Follow the rules for simplifying square roots.