Solving Rational Inequalities

Which of the following uses one of the symbols >, <, ≥, and ≤?

• rational inequality

• rational equation

• rational expression

• rational function

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

What is the first step in solving a rational inequality?

• Rewrite the inequality so that zero is on one side.

• Solve the inequality immediately.

• Rewrite the inequality so that zero is on both sides.

• Reverse the inequality sign.

How many elements are there in the solution set of a rational inequality?

• no element

• one element

• two element

• infinitely many elements

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

What is the solution set of $\frac{2x-7}{x-5}\le3?$  

•  $x>5\ or\ x\ge8$  

•  $x<5\ or\ x\ge8$ 

• $x>5\ or\ x\le8$

• $x<5\ or\ x\le8$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.APR.D.7

Solve the rational inequality  $\frac{3x+1}{x+4}<1$ .

•  $\left(-4,\frac{3}{2}\right)$  

•  $\left(-4,-\frac{3}{2}\right)$  

•  $\left(\frac{3}{2},4\right)$  

•  $\left(-\frac{3}{2},4\right)$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

What is the solution set of the rational inequality  $\frac{3}{2-x}\le\frac{1}{x-4}$ ?

•  $\left\{-4<x\le-\frac{5}{25}\right\}\cup\left\{x>2\right\}$  

•  $\left\{x<-4\right\}\cup\left\{x>2\right\}$  

•  $\left\{x>2\right\}$  

•  $\left\{x\le-4\right\}\cup\left\{\frac{5}{2}\le x\le2\right\}$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.3

The function  $P(t)=\frac{5}{t+4}$  models the population (in hundreds) of town P in terms of the number of years t elapsed since 2016. Similarly, the population (in hundreds) of a nearby town Q is modeled by the function  $Q(t)=\frac{10t}{3t−2}$ . Determine the time period when the population of Q exceeds that of P.

• after 8 months

• after 1 year

• before 1 year

• before 8 months

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

A manufacturer is producing special candles. The average cost of producing x candles is given by  $C(x)=\frac{500}{x+10}$ . How many candles should be produced for the average cost per candle to be at most ₱20?

• 10 or less

• 10 or more

• 15 or less

• 15 or more

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

The average cost of producing x T-shirts is given by  $P(x)=2400x−40$ . How many T-shirts should be produced for the average cost of each T-shirt to be at least ₱15?

• 40

• 0

•  $40<x\le100$  

• 100

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.D.12

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

Which of the following is the solution set of $\frac{5x-8}{x-5}\ge2?$  

•  $\left\{x\le-\frac{2}{3}\right\}\cup\left\{x\ge5\right\}$  

•  $x\le5$  

•  $x\le-\frac{2}{3}$  

•  $x>5$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2