Solve the compound inequality -1 ≤ 3 – 2x < 11?

Question

Write the solution set in interval notation
There is a graph that I will be attempting..
any ideas?

Answer 1

Hi Dear Schnitzel
-1 ≤ 3 – 2x < 11
It is our inequality

Part One;
-1 ≤ 3 – 2x
-1 -3 ≤ -2x
-4 ≤ -2x
{ multiply by -1 }
+4 ≥ +2x
4/2 ≥ x
2 ≥ x
x ≤ 2 Or ( - ∞ , +2]
Part Two;
3 – 2x < 11
-2x < 11-3
-2x < +8
{ again multiply by -1}
2x > -8
x > -8/2
x > -4 Or ( -4 , +∞)
................................................................................................

So ( - ∞ , +2] U ( -4 , +∞)

Good Luck ...

Answer 2

-1 <= 3 - 2x < 11 (Subtract 3 from each)
-4 <= -2x < 8 (Divide each by -2 and reverse signs)
2 >= x > -4
x is less than or equal to 2 and greater than -4
QED

Answer 3

-1 ≤ 3 – 2x < 11?

this exp[ression is true for a range of values of x from 2 to (but not including ) -4

Answer 4

-1 <= 3 - 2x < 11
-4 <= -2x < 8
2 >= x > -4

ANS : [2,-4)

for a graph, go to www.quickmath.com

Answer 5

one million) 2x+5_<11 and four(x-one million)+12_>0 2x _< 11 - 5 and 4x - 4 + 12 _> 0 2x_< 6 and 4x _> -8 x _< 6/2 and x_> 8/4 x_<3 and x_>2 answer: {x belongs to R | 2<_x_<3} 2) 5-2x>-3 or 3(6-x)<2(x-6) -2x > -3-5 or 18 - 3x < 2x - 12 -2x > -8 or -3x - 2x < -12 - 18 x <-8/-2 or -5x < -30 x < 4 or x > -30/-5 x < 4 or x > 6 answer: {x components of R| 4>x>6} 3) 3x>4-x or 2(x+3)>5x-3 3x + x > 4 or 2x + 6 > 5x -3 4x > 4 or 2x - 5x > -3 -6 x > 4/4 or -3x > -9 x > one million or x <-9/-3 x > one million or x < 3 answer: {x belongs to R | one million< x < 3} ><

Answer 6

Start off adding 3 to EVERYTHING in order to colve for x.

Once that is completed, divide everything by -2 to isolate the variable in order to solve for x.

Graph accordingly.

Answer 7

3-2x>=-1
-2x>=-4
2x<=4
x<=2
3-2x<11
-2x<8
-x<4
x>4
x<=2 nd x>4
x=-nfinity to 2 inxluding 2
x greater than 4
x={-infinity,2]U(11,infinity)

Answer 8

-1 greater than or equal to x >7
there you go