Free Printable INEQUALITIES AND NOTATION

1.

Write the following solution in interval notation:

x ≥ -3

a)

[ -3, ∞ )

b)

( -3, ∞ )

c)

( -∞ , -3 )

d)

( -∞ , -3]

2.

Write the following solution in interval notation:

z < 20

a)

( +∞ , 20 )

b)

( 20,∞)

c)

( -∞ , 20)

d)

( 20, -∞ ]

3.

Why do I draw a closed circle when it's less than or equal to or greater than or equal to?

a)

Because we are INCLUDING that solution

b)

Because we are NOT INCLUDING that solution

4.

Solve the inequality.

x + 5 ≤ 13

a)

[8, ∞)

b)

[18, ∞)

c)

(-∞, 8]

d)

(-∞, 18]

5.

5z - 2 < 13

a)

(3, ∞)

b)

(-∞, 3)

c)

(3, -∞)

d)

(∞, 3)

6.

Complete la propiedad:

Una desigualdad cambia de sentido...

a)

cuando se suman sus dos miembros por un mismo número negativo

b)

cuando se multiplican sus dos miembros por un mismo factor negativo.

c)

cuando se multiplican sus dos miembros por un mismo factor positivo

d)

cuando se restan sus dos miembros por un mismo número positivo.

7.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

8.

Which compound inequality is graphed above?

a)

5 < x < 9

b)

9 < x > 5

c)

5 ≤ x ≥ 9

d)

5 ≥ x ≥ 9

9.

Look at the Graph. Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

10.

Given:

x ≤ -10

Is -100 a solution?

a)

Yes, it is a solution.

b)

No, it is not a solution.

11.

If you were to graph the inequality would the arrow point to the left or right?
$x\ge9$

a)

left

b)

right

12.

$16x+4<-2x+6$

a)

$x<0$

b)

$x<\frac{1}{9}$

c)

$x<-2$

d)

$x<3$

13.

$-10<5x+5<20$

a)

$x>-3\ and\ x<3$

b)

$x>1\ and\ x<3$

c)

$x>-5\ and\ x<3$

d)

$x>-3\ and\ x<5$

14.

¿Qué significa un círculo hueco en la gráfica de una desigualdad?

a)

Que no se incluye el valor límite de la desigualdad

b)

Que si se incluye el valor límite de la desigualdad

15.

Resuelve: $-2<3y\ -\ 4<14$

a)

$2<y<6$

b)

$\frac{3}{5}<y<6$

c)

$\frac{2}{3}<y<6$

d)

$7<y>6$

16.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

17.

Solve:
|x + 4| - 8 > 2

a)

x > 6 and x < 10

b)

x > 6 or x < -14

c)

all real numbers

d)

no solution

18.

a)

no solution

b)

a> -1/6 or a< -5/6

c)

a>1/2 or a< -3/2

d)

all real numbers

19.

a)

all real numbers

b)

no solution

c)

0 < v < 6⁄7

d)

0 ≤ v ≤ 6/7

20.

Which of the following is the solution of the given Quadratic Inequality?

a)

5 < y < 12

b)

7 < y < 10

c)

8 < y < 9

d)

6 < y < 11

21.

Which of the following is the solution of the given Quadratic Inequality?

a)

x < -5 or x > -4

b)

x > -5 or x < -4

c)

x < 5 or x > 4

d)

x > 5 or x < 4

22.

Which of the following is the solution of the given Quadratic Inequality?

a)

-4 ≤ d ≤ -3/2

b)

3/2 ≤ d ≤ 4

c)

-4 ≤ d ≤ 3/2

d)

4 ≥ d ≥ 3/2

INEQUALITIES AND NOTATION

Total questions: 22

Worksheet time: 2hrs 37mins

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