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Fast Track - Absolute Value Equations & Inequalities

Total questions: 20

Worksheet time: 37mins

Name
Class
Date
1.
Solve:
3 | 2x + 7| + 7 < 4
a)
x < -3 and x > -5/3
b)
x < -3 and x > -4
c)
all real numbers
d)
no solution
2.
a)
no solution
b)
a> -1/6 or a< -5/6
c)
a>1/2 or a< -3/2
d)
all real numbers
3.
What is the reason that absolute value is always written as a positive?
a)
Absolute value is talking about numbers so it must be positive.
b)
Absolute value does not always have to be positive.
c)
Absolute value is like a clock it has only positive numbers.
d)
Absolute value is talking about distance, distance is always measured by positive numbers.
4.
What's a way to define absolute value?
a)
The value of a number
b)
The opposite of a number
c)
The distance of a number from zero
d)
The multiplicative inverse of a number
5.

An extraneous solution is

a)

not a concern when solving absolute value equations

b)

an apparent solution that must be rejected because it does not satisfy the original equation

6.

Solve the inequality 3<5x-2<7

a)

1<x<9/5

b)

x>9/5

c)

-1>x>-9/5

d)

1<x<9

7.

Solve the inequality 7x-3>18 or 3x-2≤-2

a)

x<3 or x≥0

b)

x>3 or x≤0

c)

x>3

d)

x>3 or x≤-3

8.

What is the solution of ∣5x-2∣=7x+14?

a)

x=-1

b)

x=-1, x=-8

c)

x=-8

d)

no solutions

9.

What is the solution of ∣x-2∣=4x+8?

a)

x=-10/3 and x=-6/5

b)

x=-10/3

c)

x=-6/5

d)

no solution

10.

What is the extraneous solution of ∣5x-2∣=7x+14?

a)

x=-1

b)

x=1

c)

x=-8

d)

x=8

11.
Write an inequality for Graph 3.
a)
x ≤ -2 AND x > 5
b)
x ≤ -2 OR x > 5
c)
x ≥ -2 OR x < 5
d)
-2 ≤ x < 5
12.
Solve: 
-4x + 1 ≤ 21 and 5x + 2 < 22
a)
x > -5 or x ≤ 4
b)
x ≥ -5 or x < 4
c)
x > -5 and x ≤ 4
d)
x ≥ -5 and x < 4
13.
4|5x-2|+7>39
a)
-6/5<x>2
b)
x=2 or x=-6/5
c)
x=2 and x=-6/5
d)
x<-6/5 or x>2
14.

What is the solution to -1 - 10a < -1 or 10 + 3a < -5 in interval notation?

a)

[-5, 0)

b)

(-5, 0)

c)

(-infinity, -5] U (0, infinity)

d)

(-infinity, -5) U (0, infinity)

15.

What is the solution to -36 < 3p - 6 < -15 in interval notation?

a)

(-10 , -3)

b)

[-10 , -3)

c)

(-infinity, -10) U (-3, infinity)

d)

(-infinity, -10] U (-3, infinity)

16.

There are 10 less trumpet players than saxophone players. The number of saxophone players is 3 times the number of trumpet players. How many trumpet players are there?

a)

15 trumpet players

b)

10 trumpet players

c)

5 trumpet players

d)

20 trumpet players

17.

The larger of two numbers is 12 more than the smaller number. If the sum of the two numbers is 74, find the two numbers.

a)

12 and 24

b)

31 and 43

c)

24 and 36

d)

51 and 63

18.

The length of a rectangle is 3 inches more than its width. If the perimeter is 42 inches, find the dimensions of the rectangle.

a)

9 in by 12 in

b)

3 in by 14 in

c)

10 in by 11 in

d)

8 in by 13 in

19.

The length of a rectangle is 5 less than twice its width. The perimeter is 26 meters. Find the dimensions of the rectangle.

a)

5 m by 8 m

b)

3 m by 10 m

c)

4 m by 9 m

d)

6 m by 7 m

20.

Convert the equation y= 5x2 - 40x + 67 into vertex form.

a)

y= -5(x + 4)2 + 13

b)

y= 5(x + 4)2 - 13

c)

y=5(x - 4)2 - 13

d)

y= 5(x - 13)2 + 4