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

gueesstt
Apr 22, 2018

#1**+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

GYanggg
Apr 22, 2018

#1**+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