Question 477945
the best way to solve these is to break them up into segments and then combine the answers at the end.
question number 1:
6 > x + 4 > 4
break this up into:
6 > x + 4
x + 4 > 4
solve each separately:
subtract 4 from both sides of 6 > x + 4 to get 2 > x
subtract 4 from both sides of 2 + 4 > 4 to get x > 0
if 2 > x then x < 2
if x > 0 then 0 < x
combine this answer into:
0 < x < 2
plug a value of x that is greater than 0 and less than 2 into the original equation and you'll see that it is satisfied.
plug a value of x that is not greater than 0 or is not less than 2 into the original equation and you'l see that it is not satisfied.
question number 2:
2x > x > 10 > -x
break this up into:
2x > x
x > 10
10 > -x
solve each separately.
subtract x from both sides of 2x > x to get x > 0
leave x > 10 as is
multiply both sides of 10 > -x by -1 to get -10 < x
this is the same as x > -10
multiplying both sides of an inequality by a negative number reverses the inequality.
combine this answer into:
x > 10 because if x > 10 then it satisfies x > 0 and it satisfies x > -10.
if you substitute into the original equation of 2x > x > 10 > -x, you'll see that if x > 10 then the equation is satisfied and if x <= 10 the equation is not satisfied.
question number 3:
abx = c 
divide both sides of this equation by ab to get:
x = c/ab
question number 4:
a + bx = c + dx
subtract dx from both sides of this equation to get:
a + bx - dx = c
subtract a from both sides of this equation to get:
bx - dx = c - a
factor out the x to gtet:
(b-d)x = c-a
divide both sides of this equation by (b-d) to get:
x = (c-a)/(b-d)
question number 5:
ax - x = bx + c 
subtract bx from both sides of this equation to get:
ax - bx - x = c
factor out the x to get:
x(a - b - 1) = c
divide both sides of this equation by (a-b-1) to get:
x = c/(a-b-1)