2.6 Solve the rational equation & inequalities
Learn how to solve rational equalities & inequalities by watching the video
Rational Equalities : https://www.youtube.com/watch?v=1fR_9ke5-n8
Rational Inequalities: https://www.youtube.com/watch?v=gfnVHwhEe6U
1) Solve the following equalities
𝑥
1
a)
b)
=
32
18𝑥
3
12
−
=2
𝑥−2 𝑥−3
c)
1
1
≤
𝑥 2𝑥 − 1
c)
𝑥+4=
𝑥+2
𝑥−5
2) Solve the following inequalities
a)
𝑥−4
>0
2𝑥 + 1
b)
𝑥 2 − 2𝑥 − 3
≤0
𝑥 2 + 2𝑥 + 1
2.7. Use linear, quadratic, and rational equations to solve real-life problems.
Solve the following problems
2
1) A picture frame has a total perimeter of 3 meters. The height of the frame is 3 times its width.
a) Draw a diagram that represents the problem. Identify the width as 𝑤 and the height as ℎ.
b) Write h in terms of 𝑤 and write an equation for the perimeter in terms of 𝑤.
c) Find the dimension of the picture frame.
2) The total cost for printing small booklets is $500 (the fixed cost) plus $2 for each booklet
printed.
a) Express the total cost, 𝐶(𝑥) of producing booklets as a function of the number of booklets,
𝑥.
b) Complete the following table
𝐶(𝑥)
𝑥
Number of booklets
In dollars
0
50
100
150
200
c) Create a graph of 𝐶(𝑥) on the Cartesian Coordinate
d) If the total cost of producing booklets is $1,600, how many booklets were produced?
3) A rectangular play yard is to be enclosed with a fence on three of its sides and a brick wall on the
fourth side. If 120 feet of fencing material is available, what dimensions will yield the maximum
area?