Question

What is the reason for each step in the solution of the inequality? −2(x+3)−4>4x+30

Answer 1

Distribute the -2 to the (x+3) because of distributive property
-2x-6-4>4x+30
add like terms because you aren't changing anything
-2x-10>4x+30
add 2x to both sides (addition property of equality,  when b=b and a=a, a+b=a+b)
also addative inverse, a+(-a)=0, the 2x canceld the -2x
-10>6x+30
minus 30 from both sides (subtraction property of equality again) and addative inverse, the -30 cancleled the 30
-40>6x
divide both sides by 6 (division property of equality)
-20/3>x
property of 1 division (if a=a then a/a=1
x<-20/3

Answer 2

You would have to first distribute the -2 to the x+3 which gives you -2x-6.  Then you would subtract the 4 which gives you -2x-10 on the left side.  Now you have the equation -2x-10>4x+30.  Move the 4x to the other side giving you         -6x-10>30.  Now add the 10 from the other side which leaves you with -6x>40.  Now remember when you divide by a negative in an inequality, you HAVE TO flip the sign giving you the answer of x<-20/3.