Inequalities

Two Step Inequalities

100

(-3/4)x > -12

x<16

200

(2/3)x + 3 > 11

x>12

300

6>=(7/3)x - 1

x<=3

400

(3/5)x - 2 > (6/5)x + (3/5)

x<-13/3

500

(w+3)/2 < -8

w < -19

Multi-Step Inequalities

100

7-3x<16

x>-3

200

3x + 1.2 < 7x-1.3

X>.625

300

2x+10 >= 7(x+1)

x<= 3/5

400

-2(x+3) < 4x-7

x>1/6

500

2(y-2)>-4+2y

no solution

Compound Inequalities

100

Write an inequality representing the set of numbers. All real numbers that are greater than or equal to -2 and less than 3.

-2<=x<3

200

-2<-2-x<1

0>x>-3

300

3x+1<4 or 2x - 5>7

x<1 or x>6

400

2 <2x - 3< 4

5/2 < x < 7/2

500

0.5n>-2 or 2n-2<6+n

n is any real number

Absolute Value Inequalities

100

|x-4|<3

1<x<7

200

|2x+3|>4

x<-3.5 or x>0.5

300

|2x+1|-3>=6

x>=4 or x<= -5

400

|5x+3| - 4> 9

x<-3.2 or x>2

500

6|x+3| - 4 < 20

-7<x<1

Word Problems

100

Four more than the quotient of a number and three is at least nine.

(n/3) + 4 >=9 n>=15

200

There is a rectangle whose length is 9 meters and width is x meters. What values of x make the area greater than 36 square meters.

x> 4 meters

300

You have $18.50 to spend on a pizza. It costs $14 plus $0.75 for each additional topping, tax included. Find the maximum number of toppings the pizza can have.

0.75x + 14 <= 18.50 6 toppings

400

In 1958, the painting of the Mona Lisa was sold at auction for $252,000. The painting was auctioned again in 2000 for 3 million dollars. Write a compound inequality to represent the different values that the painting probably was worth between 1958 and 2000.

$252,000 <= x <= $3,000,000

500

The test scores in the class range from 60 to 100. Write an absolute value inequality describing the range of test scores.

|x-80|<=20