# Zero Factor Property and Inequalities

The zero factor property:

A) p^2 - p = 42

B) 16x - x^3 = 0

C) (x + 2)(x + 3) = 20

Solve each equation for y. Assume a and b are positive numbers:

D) y^2 + ay + by + ab = 0

Applications:

E) Tennis court dimensions. In singles competition, each player plays on a rectangular area of 117 square yards. Given that the length of that area is 4 yards greater than its width, find the length and width.

F) More missing numbers. The sum of two numbers is 6.5, and their product is 9. Find the number.

G) Ski jump. The base of a ski ramp forms a single triangle. One leg of the triangle is 2 meters longer than the other. If the hypotenuse is 10 meters, then what are the lengths of the legs?

Inequality symbols. Determine whether each inequality is true or false:

H) (-1)(-3) < (-1)(5)

Interval Notation and Graphs. Write the solution set in interval solution and graph it:

I) x <30

Solving Linear Inequalities. Fill in the blank with an inequality symbol so that the two statements are equavilent:

J) 2x - 3<= - 4

Solve the inequalities. Express the solution set in interval notation and graph it.

K) 5 - (1/3)x >3

Applications. Identify the variable and write an inequality that describes each solution.

L) Rita will not take less than $12,000 for the car.

Solve each problem by using an inequality

M) Sewing machines. Charles wants to buy a sewing machine in a city with a 10% sales tax. He has at most $700 to spend. In what price range should he look?

N) C or better. Professor Brown counts her midterm as 2/3 of the grade and her final as 1/3 of the grade. Wilbert scored only 56 on the midterm. If Professor Brown also uses the grading scale given in the table then what range of scores on the final exam would give Wilbert a C or better in the course?

GRAPH

GRADING SCALE

90-100 A

80-89 B

70-79 C

60-69 D

Graphing the solution set. Graph the solution set to each compound inequality

O) x >3 or x <-3

Solve each compound inequality. Write the solution set using intervale notation and graph it

P) 5 <x or 3 - (1/2)x <7

Solve each compound inequality. Write the solution set in interval notation and graph it.

Q) 0 < (3 - 2x)/2 <5

Write each union or intersection of intervals as a single interval if possible

R) (-3,infiinty symbol) u (-6,infinity symbol)

Write either a simple or a compound inequality that has the given graph as its solution set....

S) ______________] (___________________

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

Selling price range.

T) Renee wants to sell her car through a broker who charges a comission of 10% of the selling price. The book value of the car is $14,900 but Renee still owes $13,104 on it. Although the car is in only fair condition and will not sell for more than the book value, Renee must get enough to at least pay off the loan. What is the range of the selling price?

Absolute Value equations

U) |3 - (3x/4)| = (1/4)

Solve each absolute value equation:

V) 3 - (1/2)|(1/2) x - 4| = 2

Write an absolute value inequality whose solution set is shown by the graph.

W) _____]_____________________[_____

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Determine whether each absolute value inequality is equialent to the inequality following it

X) | x - 3| > 0,x - 3 >0

Solve each absolute value inequality and graph the solution set

Y) |3x|<21

All or nothing Solve each absolute value inequality and graph the solution set

Z) |5 - x| + 5 > 5

#### Solution Summary

The following posting helps with problems involving the zero factor property and inequalities.