CPhill

x(x -3) < 4     simplify the left and add 4 to both sides

x^2 -3x -4 < 0      factor

(x - 4)(x + 1) < 0

Now...the answer comes from either this interval (-1, 4)  or from these two intervals (-∞, -1) and (4, ∞)

Let's test 0 on the interval (-1, 4) in the factored form..we have

(0 -4) ( 0 + 1) < 0

(-4)(1) < 0    

 -4 < 0   and that's true    .....

So....the answer is  x = (-1 , 4)

Here's a graph of  x^2 -3x -4  which  confirms that this function is less than 0 on ( -1, 4).....

Very nice, Melody  !!!!!

1/4 = 25%

So

25% + 48% = 73%

So

100% - 73% =  27% liked some other class best

We can use this "formula"

 [20000 - 13750] / 20000 =

6250/20000 = .3125 =  a 31.25% decline in value

9(3-2x)=2(10-8x)      simplify

27 - 18x = 20 - 16x      add 18x to both sides, subtract 20 from both sides

7 = 2x           divide both sides by 2

7/2 = x

y = 8x - 1

Let x be the first number and 36 - x be the second number

So we have

x - (36 -x) = 2    simplify

2x - 36 = 2      add 36 to each side

2x = 38           divide both sides by 2

x = 19      and that's one number

And 36 - 19 = 17    and that's the other number

Distance / Time = Rate  .....so.....

(1 + 2/9) mi / (1 + 1/7) hr =

(11/9) mi / (8/7) hr =

11/9 x 7/8  = 

77/72  mi/ hr =

about 1.07 mi/hr 

Well.....if you don't want it "simplified"......what's the question????......we'll just leave it, as is......

There is a "formula" for this given by

S_n = (a₁)(1 - r^n) / ( 1 - r)      where Sn  is the sum  of the first n terms, a₁ is the first term, and r is the common ratio (1/3, in our case)

So we have

S₇  =  (1/3) [(1 -(1/3)^7 ] / [ 1 - (1/3) ] =  (1/3) [ 1 - 1/2187 ] / (2 /3) = [1 - 1/2187] / 2 = 1093/2187 = about  .49977 ≈ .5