Math help please :c?

Write an inequality for each statement,then solve the inequality.








Six is less than or equal to the sum of 4 and -2x.





The product of 4 and the sum of a number and 12 is at most 16.





The sum of half a number and two-thirds of the number is less than 14.








Please help I've been stuck on these for about 45 minutes now.





:c

Math help please :c?
1 question:


6 ≤ -2x + 4


6 - 4 ≤ -2x


2 ≤ -2x


-1 ≥ x





* note: the equality sign is swapped because when you divide or multiply a number by a negative, then the equality sign changes.





2nd question:


4(x+12) ≤ 16


4x + 48 ≤ 16


4x ≤ -32


x ≤ -8





3rd question:


(x/2) + (2x/3) %26lt; 14


7x/6 %26lt; 14


7x %26lt; 84


x %26lt; 12





I hope that helps!
Reply:6 %26lt;= 4 + (-2x)


6 - 4 %26lt;= -2x


2 %26lt;= -2x


1 %26gt;= x or x %26lt;= 1





4 * (x + 12) %26lt;= 16


4x + 48 %26lt;= 16


4x %26lt;= -32


x %26lt;= -8





1/2 N + 2/3 N %26lt; 14


3/6 N + 4/6 N %26lt; 14


7/6 N %26lt; 14


7N %26lt; 14*6 ( = 84 )


N %26lt; 12
Reply:First:





6 %26lt;= 4-2x


6-4 %26lt;= -2x


2 %26lt;= -2x


1 %26lt;= -x


x %26gt;= -1


--------------------------------------





Second:





Let a number be x,





4x + (x + 12) %26lt;=16 {less than equals to imples atmost}


5x + 12 %26lt;= 16


5x %26lt;= 16-12


5x %26lt;= 4


x %26lt;= 4/5





Third:





Let the number be x,





x/2 + 2x/3 %26lt; 14


Taking LCM


(3x+4x)/6 %26lt; 14


7x/6 %26lt; 14


7x %26lt; 14*6


x %26lt; (14*6)/7


x %26lt; 12








I am abit confused with sequencing of second statment "The product of 4 and the sum of a number and 12". If anyone can verify this.