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

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

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