solve the inequality 3/(x+2)<4 help?!?

Question

i need to slove the inequality: 3/(x+2)<4 and then graph it on a number line. please help me!!!

Answer 1

multiply both sides by 3 which cancels the 3 on the left and makes the 4 a twelve then subtract 2 on both sides and you are left with x<10 on a number line you would draw an open circle at the 10 because its not included and make a solid line down the number line to everything below 10. It just means the answer can below ten but not equal to 10.

Answer 2

First, assume x+2 > 0.

Then, multiply both sides by x+2 and get
3 < 4(x+2)
3 < 8x + 8
-5 < 8x
-5/8 < x
So x > -5/8. We assumed x > -2, so that means we cannot have -2 < x <= -5/8.

Now, assume x+2 < 0. Multiply both sides by x+2 an dget
3 > 4(x+2)
(same steps as before, with < replaced by >)
and you get x < -5/8. But we already assumed x < -2, so the inequality is always true with this assumption.

We cannot have x = -2, because then we're dividing by zero.

Therefore, the solution is x < -2 or x > -5/8.

To graph this on a number line, draw open circles at x=-2 and x=-5/8. Then draw a horizontal line to the left of the open circle at x=-2, and another horizontal line to the right of the open circle at x=-5/8.

Answer 3

3/[x+2]<4
3<4[x+2]
4x+8>3
4x>-5
x>-5/4
on the x-axis plot -1.25 and draw
a vertical line through the point.
All the area to the right of this line
pertains to this inequality.

Answer 4

3/(x+2)<4 multiply by x+2
3<4(x+2) (this is valid if & only if x+2>0 or x>-2)
3<4x+8 subtract 8
-5<4x divide by 4
x>-5/4 Since x>-5/4 requires that x>-2, this is valid.

Answer 5

(5x-3)/(x+3) ? 4 sparkling up the equation as though the ? is an = sign (5x-3)/(x+3) ? 4 multiply through via (x+3) to do away with the fraction (5x-3) ? 4(x+3) 5x-3 ? 4x+12 subtract 4x from the two facets x-3 ? 12 upload 3 to the two facets x ? 15, x would not equivalent -3

Answer 6

3/(x+2)<4
3<4(x+2)
3<4x +8
(-5)<4x
(-5/4) < x

Answer 7

ya u can solve it as follows:
3/(x+2) <4
3 < 4(x+2)
3< 4x+8
4x> -5
or x > -5/8
ok this is your equation which is to be plotted on number line..
now ur area will be
wherever u have -5/8 on a number line,then the area to the right of this will be ur required area..

Answer 8

3<4x+8
4x+8>3
4x>-5
x>-5/4

Answer 9

You've got a lot of conflicting answers here! Who are you going to believe?

Answer 10

3/(x+2) < 4
3/4 < x+2
x > -1.25

..............|x-->
-2............. -1............. 0............. 1............. 0