SOLUTION: Please show me how to solve the following inequalities for X: 1. 6 > x + 4 >4 2. 2x > x > 10 > -x Also the next category says Solve each of the following for x in terms of

Question 477945: Please show me how to solve the following inequalities for X:
1. 6 > x + 4 >4
2. 2x > x > 10 > -x
Also the next category says Solve each of the following for x in terms of other variables. (Assume none of the variables equals zero)...
3. abx = c
4. a + bx = c + dx
5. ax - x = bx + c
Many thanks for your help. I was getting a migrane trying to solve this!!!!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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)

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