please help me

Question

solve the compound inequality: 8≤3/4(2x+5)≤6

Answer 1

8 ≤ 3/4(2x+5) ≤ 6      avoid working with fraction so multiply the whole equation by 4

32 ≤ 3(2x+5) ≤ 24    Now distribute 3

32 ≤ 6x+15 ≤ 24      subtract 15 to front and back

32-15 ≤ 6x ≤ 24-15  simplify

17 ≤ 6x ≤ 9              now divide by 6 to front and back

17/6  ≤ x ≤ 9/6         simplify

17/6 ≤ x ≤ 3/2

Answer 2

First of all, are you sure you wrote the equation down properly?  Because no number if both bigger than 8 and smaller than 6.  Therefore, there is no answer to the equation as written.  However, given the equation the way it's written, this is how you would solve it.

 

It's easiest to set it up as two separate equations.  8≤3/4(2x+5) AND 3/4(2x+5)≤6. 

 

Now distribute the 3/4 in the first equation:  8≤3/4*2x + 3/4*5.  That gives you 8 ≤ 1.5x + 3.75.

 

Subtract 3.75 from both side to get the 1.5x by itself.  4.25 ≤ 1.5x.

 

Divide both sides by 1.5 to get the x by itself.  2.833 ≤ x.

 

Now you do the same with the second equation.  3/4(2x+5)≤6.

 

1.5x + 3.75 ≤ 6.     1.5x ≤ 2.25   x ≤ 1.5

 

Finally write it all as one equation with the x in the middle.  2.833 ≤ x ≤ 1.5.

 

Again, x cannot be bigger than 2.8 AND smaller than 1.5, so the numbers don't actually work.