Alegebra Help?

Question

These are linear Inequalities,
Solve for x. Collect xs on the Left side. The sloution should be presented with x first, the correct inequality symbol, then the number
x+4-8x-1>3(x-2) let me add that the sign ">" in this problem has a line under it as well. Can you please explain this problem as well. THANK YOU SO MUCH

Answer 1

x + 4 - 8x - 1 ≥ 3.(x - 2)
3 - 7x ≥ 3x - 6
9 ≥ 10 x
x ≤ 9 / 10

Answer 2

OK, so we start with -8x +x + 4 - 1 >= 3(x - 2). You can combine like terms on the left and multiply out the parentheses on the right to get -7x + 3 >= 3x - 6.

Now, you're supposed to collect x's on the left, so you need to get rid of them on the right. Subtract 3x from each side and you get -10x +3 >= -6. Now, subtract 3 from each side and you get -10x >= -9.

OK, here's the tricky part. We're fixing to divide both sides of the equation by a negative number. When you do that, you have to turn the inequality sign around.

Divide both sides by -10 and you get x <= 0.9. That means that 0.9 and all numbers smaller than 0.9 are solutions to the inequality.

Answer 3

x+4-8x-1 ≥ 3(x-2)

Expand the right hand side:
x+4-8x-1 ≥ 3x - 6

Gather like terms on the left hand side:
-7x + 3 ≥ 3x - 6

Add 7x to each side:
3 ≥ 10x - 6

Add 6 to each side:
9 ≥ 10x

Divide each side by 10:
9/10 ≥ x

Reverse the equation to present the x first, remembering to always "let the alligator's open mouth eat the bigger number"
x ≤ 9/10

Answer 4

x+4-8x-1>3x-6
x-8x--3x>-4+1-6
-10x>-9
x<-9/-10
x<+9/10
when you have another line under *>* that means that it is bigger or equals that value and in the *<* it means smaller (less)than or equals
which means in this case:
x is smaller than or equals 9/10

Answer 5

3-7x>3x-6
-10x>-9
x<9/10