Rational Equations and Inequalities
Radical Equations and Inequalities
Extraneous Solutions
Absolute Value Inequalities
f(x) = g(x)
100
This is the lowest common denominator for this rational equation.
`1/5=1/(5m)+(5m-5)/m`
What is 5m?
100
Find x:
`3sqrt(2x)=12`
What is x = 8?
100
Which of these solutions: x = 2, x = 3 is extraneous for this rational equation?
`x/(x-1)-1/(x-2)=(2x-5)/(x^2-3x+2)`
What is x = 2?
100
Find the solution of the following inequality.
`|n/4|≤3`
What is
`-12≤n≤12?`
100
Approximate the point that these two lines intersect.
What is ~(5.5, 6.2)?
200
The lowest common denominator for this equation can be broken down into `(p+1)` and what other factor?
`(p+5)/(p^2+5p+4)=5/(p+1)-1/(p+1)`
What is
`(p+4)?`
200
Find x:
`sqrt(5x+1)=sqrt(4x+3)`
What is x = 2?
200
What values of x would yield an extraneous solution for this equation?
`2/(x^2-x)=1/(x-1)`
What are x = 0 and x = 1?
200
Which of the following numbers does not belong in the solution of this inequality?
`|-9v| ≤ 54`
a) -5
b) 7
c) 4
d) 1
What is b) 7?
200
I earn $40 a week mowing lawns around my neighborhood, and my lawnmower stops working after 12 weeks. If my sister makes $30 a week babysitting, how many weeks will it take her to make as much money as I did?
What is 16 weeks?
300
This is the lowest common denominator for the following rational equation.
`1/(k+5)-(k+4)/(k^2-k-30)=1/(k-6)`
What is
`k^2-k-30?`
300
Find y:
`(5y+2)^(1/3)-3=0`
What is y = 5?
300
Find the extraneous solution for this equation:
`4/x+1=(2x+2)/x`
What is x = 0?
300
Find the solution to the following inequality:
`|10+4x|<14`
What is -6 < x < 1?
300
Find the point at which these two functions intersect:
`y=1/2x^3-4`
`y=-2x+4`
What is (2,0)?
400
The lowest common denominator for this rational equation can be broken down into `(x+2)` and what other factor?
`(4x+20)/(x^2-3x-10)+2/(x+2)=(x-2)/(x^2-3x-10)`
What is
`(x-5)?`
400
Find x:
`sqrt(x+2) = x-4`
What is x = 7?
400
Find the solutions to the following equation. Identify which ones are extraneous.
`sqrt(4x+13) =x+2`
Real Solution: x = 3
Extraneous Solution: x = -3
400
Which of the following numbers does belong in the solution of this inequality?
`|2+3x|/2≥5`
a) 2
b) 3
c) -3
d) 0
What is b) 3?
400
Create two functions that intersect at the point (2,4).
Examples include:
`y=x^2`
`y=3x-2`
`y=|-2x|`
500
WHITEBOARDS!
Solve the following rational equation:
Find the lowest common denominator (100 pts), arithmetic solutions (200 pts) and any extraneous solutions (200 pts).
`x/(x-2)=4/(x^2-8x+12)-1/(x-6)`
LCD:
`x^2-8x+12`
Arithmetic solutions: x = -1, x = 6
Extraneous solutions: x = 6
500
Find x:
`3(2x+4)^(4/3)=48`
What are x = 2 and x = -6?
500
True or False: This equation has at least one extraneous solution.
`(x-3)/(2x+1)+(4x)/(3x+5)=(7x^2+12x-20)/(6x^2+13x+5)`
What is false?
500
Find the solution for the following inequality.
`8+|4v-7|≥17`
`v≥4`
or
`v≤-1/2`
500
Using your calculator, find one of the points of intersection between these two functions.
`y=sqrt(x-4)+1`
`y=(x-3)^3`
What is (4,1)?