9x-1 < 3/4 (16x-2)?

Question

could you show all necessary steps to the solution, i want to make sure i included all of them.

Answer 1

9x - 1 < 3/4 (16x-2)
Multiply out the constant on the right:
<=> 9x - 1 < 12x - 3/2
Group the x terms and the constants:
<=> 9x - 12x < -3/2 + 1
Simplify:
<=> -3x < -1/2
Divide through by -3, remembering to change the direction of the inequality because we're dividing by a negative number:
<=> x > 1/6.

Answer 2

first you will desire to distribute the three/4 in the process the (16x-2) to get (12x-3/2) so which you will desire to have 9x-a million<12x-3/2 next subtract the 9x from the two factors so which you will desire to have -a million<3x-3/2 next upload 3/2 to the two factors so which you will desire to get a million/2<3x next divide the two factors by 3 so which you will desire to get a million/6

Answer 3

clear the fraction:

9x-1<12x-3/2

collect all x terms together by subtracting 12x from both sides and collect all numbers together by adding 1 to both sides to get:

-3x<-1/2

get x by itself on one side by multiplying both sides by 1/3:

-x<-1/6

now clear the minus signs by multiplying both sides by -1 (note when you multiply by a negative number, your inequality reverses)

x>1/6

Your original inequality is true for all x greater than 1/6

Answer 4

9x - 1 < 3/4 (16x -2)
-----------------multiply both side by 4
4(9x-1) < 3(16x-2)
36x - 4 < 42x - 6
42x - 36x > 6 - 4
6x > 2
x > 1/3

Answer 5

9x-1<12x-3/2
-1+3/2<12x-9x
1/2<3x
1/6