When 4 times a number n is decreased by 3 its at most 22.

Question

I just need some help with my homework.

Answer 1

So take 4 times a number n

 

4n

 

now decrease it by 3

 

4n - 3

 

and the greatest it can be is 22, but it can be less

 

4n - 3 ≤ 22

 

Now solve for n

 

4n - 3 ≤ 22

4n ≤ 25

n ≤ 25/4

n ≤ 6.25

 

Answer 2

"When 4 times a number" meaning → 4n

"is decreased by 3" meaning → we subtract 3 from that

"it's at most 22" meaning → it can be equal to 22, it can be less than 22, but not more.....

 

so we get:

4n - 3 ≤ 22                       inequalities can be solved just like equations*

4n      ≤ 25                       add 3 to both sides

n        ≤ 25/4, or 6.25      divide both sides by 4

 

*The main difference between solving inequalities and equations is that if you × or ÷ both sides of an inequality by a negative number, then you change the direction of the inequality sign.

 

For example:

-3n ≤ 27

n    ≥ -9

Notice that 4 ≥ -9, and -3 × 4 = -12 and -12 ≤ 27