Solve simple Absolute Value Inequality

 Exam - BARTON COLLEGE PRACTICE PLACEMENT TEST Ex. 39

Exercise:

The inequality |8 - x| < 8   is equivalent to:

 
a) x < 0

b) x > 0

c) x<0 or x > 16

d) 0 < x < 16

 Solution

Solve the absolute value inequality:  |8 - x| < 8

We solve the inequality 8-x < 8 and the inequality -(8-x) < 8, and than find intersection between the solutions.

Solution 1 for  (8-x) >=0
8 - x < 8
8 - 8 < x
x > 0 

 

x > 0 and (8-x) >=0 is:

0 < x <= 8

Solution 2 for (8-x) <=0
-(8-x) < 8
-8 + x < 8
x < 8 + 8

x < 16

 

x <16 and (8-x) <=0 is  8 <= x < 16

The combination of solution 1 and 2 : 

 0 < x <= 8 OR   8 <= x < 16  is

 

0 < x < 16

The correct solution is d.

We can see the problem graphicaly:

 The inequality |8 - x| < 8   is equivalent to  0 < x < 16

Exercises 5- 6 Exam - BARTON COLLEGE PRACTICE PLACEMENT TEST

   Exam - BARTON COLLEGE PRACTICE PLACEMENT TEST

 Execise 5

Simplify:  

 

Solution

 The correct answer is d.

 

Execise 6

Simplify : 

Solution

 The corrcect answer is c.

Exercise 1- 4 Exam - BARTON COLLEGE PRACTICE PLACEMENT TEST

  Exam - BARTON COLLEGE PRACTICE PLACEMENT TEST

 Execise 1

Simplify:  

a) 4
b) ‐4
c) 12
d) ‐10.5

 Solution

 The order of mathematical action are:

Power & Roots
Multiplication & Division
Addition $ Substration

 So we solve the according the following rule:

 The correct answer is c.

 

Execise 2

Simplify: (2a – 4) + 2(a – 5) – 3(a+1)

a) 7a – 11
b) a – 17
c) a – 11
d) 7a ‐17

Solution

(2a – 4) + 2(a – 5) – 3(a+1)=

2a - 4 + 2a - 10 - 3a - 3 = 

2a + 2a - 3a -4 -10 -3 = 

a -17

The correct answer is b.

 Execise 3

Evaluate the expression:   , when a = 2 and b = 5

a) ‐14
b) 1
c) 66
d) 81

Solution

 we substitute a = 2 , b = 5 at the expression : 

 

 The correct answer is b.

 

Execise 4
 

Firefighters use the formula S = 0.5P + 26 to compute the horizontal range S in feet of water from a particular hose, where P is the nozzle pressure in pounds. Find the horizontal range if pressure is 90 lb.

a) 44 feet
b) 450 feet
c) 19 feet
d) 71 feet

Solution

We substitute P = 90 lb at the formula S = 0.5P + 26.

S = 0.5*90 + 26 = 45 + 26 = 71

The correct answer is d.