The quotient of a number x decreased by 4 and 7 is less than or equal to 2 or greater than or equal to 8. What is the possible solutions of x

Question

Can someone please help me with the prealgebra I realy don't understand 

Answer 1

There are 2 inequalities:

(x-4)/7<2

 

or

 

(x-4)/7>8.

 

We need to solve both.

(x-4)/7<2                   Multiply by 7 both sides

 

(x-4) < 2•7                 Simplify

 

x-4 <14                     Add 4 to both sides.

x <18.                       The solution is all numbers x less than 18.

 

We solve the second inequality the same way:

(x-4)/7>8

(x-4)>56

x>60.

 

The solution set is all numbers less than 18 and all numbers bigger than 60.

Note, that because you used the connector or we combined the two solution sets, x<18 and x>60.