Chapter 2 Equations and Inequalities

2.1 solving equations graphically

100

What is the solution of 

3x+2=17

5 is the solution 

200

are 3x+2=17 and x-2 equivilant?

yes, 5 is the only solution of each equation 

300

use the intersect method to solve the equation 

x²-1=x²+7

-2 and 2 

400

use the x intercept method to find all real solutions of the equation 

x³-8x²+9x+18=0

x= -1 and 3 and 6

500

true or false

x=r is a solution, or root, of the equation f(x)=0

true 

2.2 solving quadratic equations algebraically

100

soleve my completing the square 

x²-2x=12

x= 1+ square root of 13

x= 1- square root of 13

200

soleve by factoring 

x²-5x=14

3

300

solve by square roots 

x²=9

x=0 

x=-1.7,1.1

400

determine the nature of the square 

2x²=-x-3

no real solutions 

500

solve by quadratic formula 

x²-4x+1=0

x=2+square root of 3

x=2-square root of 3

2.3 applications of equations

100

A rectangle has a perimeter of 45 cm and an area of 112.5 square cm. What are the dementions?

8 cm and 15 cm 

200

2 cars leave a gas station at the same time, one traveling north ans the other south. The northbound car travels at 50 mph. After 3 hours the cars are 345 miles apart. How fast is the southbound car traveling?

65 mph

300

a rectangle is twice as wide as it is high. The area is 24.5in², what are the dimensions ?

h=3.5

w=7

400

a high risk stock pays 12% per year. A savings account pays 6% per year. How much of a $9,000 investment should be put in each for an 8% return?

3,000 in stock

6,000 for saving 

500

A radiator contains 8 quarts of fluid, 40% of which is antifreeze. How much fluid should be replaced with pure antifreeze so that the new mixture is 60% antifreeze?  

2.4 quarts 

2.4 other types of equations

100

find all real solutons of each equation

(2x+3)=9

-6

3

200

find all real solutions for the equation 

(x-3)=x

2

300

find all real solution of each equation 

square root of 4x + 9=0

4

400

square root of x+2=3

7

500

square root of x+7=x-5

9

2.5 inequalities

100

an interval is 

is a set of all numbers lying between 2 fixed numbers. 

200

how do you write an answer in order pairs?

(x,x)

300

express the given statement in symbols

x is non-negative 

x is greater than or equal to 0

400

solve the equation and put in interval notation 

2x+7(3x-2)is less than 2(x-1)

(-infinity, 4/7)

500

solve each inequality for x

ax-b is less than c

(-7/17,infinity)