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How many integers $n$ satisfy both of the inequalities $4n + 3 < 25$ and $-7n + 5 < 24$?

 Apr 22, 2018

Best Answer 

 #1
avatar+972 
+3

We first need to simplify both inequalities. 

 

4x + 3 < 25

 

Subtracting 3 from both sides:

 

4x < 22

 

Dividing both sides by 4:

 

x < 11/2

 

-7n + 5 < 24

 

Adding both sides by 7n and subtracting both sides by 24 (to avoid dividing by a negative number):

 

7n > -19

 

Dividing both sides by 7:

 

n > -19/7

 

n must be greater than -2 and -5/7 but also smaller than 5 and 1/2

 

The integers in between are: 

 

-2, -1, 0, 1, 2, 3, 4, and 5

 

There are 8 integers 

 Apr 22, 2018
 #1
avatar+972 
+3
Best Answer

We first need to simplify both inequalities. 

 

4x + 3 < 25

 

Subtracting 3 from both sides:

 

4x < 22

 

Dividing both sides by 4:

 

x < 11/2

 

-7n + 5 < 24

 

Adding both sides by 7n and subtracting both sides by 24 (to avoid dividing by a negative number):

 

7n > -19

 

Dividing both sides by 7:

 

n > -19/7

 

n must be greater than -2 and -5/7 but also smaller than 5 and 1/2

 

The integers in between are: 

 

-2, -1, 0, 1, 2, 3, 4, and 5

 

There are 8 integers 

GYanggg Apr 22, 2018

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