2^(x+3) - 2(x-1) = (15/2)(2^x)?

Question

help?? show that the sides are equal

Answer 1

2^(x+3) - 2^(x-1) = (15/2)(2^x)
First combine the two in the denominator with the two in the numerator on the right side. You subtract exponents.
2^(x+3) - 2^(x-1) = (15)(2^(x-1))
Divide everything by 2^(x-1)
2^(x+3)/2^(x-1) - 2^(x-1)/2(x-1) = 15(2^(x-1))/2^(x-1)
2^(x+3-(x-1)) - 1 = 15
2^(3+1) - 1 = 15
2^4 - 1 = 15
16 - 1 = 15
15 = 15

Answer 2

Those who have obtained the answer 15=15 have done so by assuming that 2(x-1) in the question should be 2^(x-1). However, if the original question is correct then one obtains
2^x = 4(x-1)
which others have obtained but rejected because the two sides are not equal. But they are equal if x=2, each side being equal to 4. So, is the term 2(x-1) correct, in which case the two sides are equal only if x=2, or should it be 2^(x-1), in which case the two sides are always equal?
If the term is 2^(x-1), then
2^(x+3) - 2^(x-1) = (15/2)2^x
and since 2^3=8 and 2^(-1)=(1/2), the equation becomes
8(2^x) -(1/2)(2^x) = (15/2)(2^x),
i.e. 8-(1/2)=(15/2) which is always true and a little shorter than some of the other proofs.

Answer 3

there is not any prefer to purchase calculator to resolve those questions,i don't think of there is any calculator to resolve algebraic issues. a million)9x-a million=-11 9x= -11+a million 9x= -10 x= -10/9 2)3x-4=13 3x=13+4 3x=17 3x=17/3 3)7x/2 +5=8 7x/2 =8-5 7x/2=3 x=6/7 4)8x/7 +9=30 8x/7 =30-9 8x/7=21 x= 147/8 5)16= -2x-a million 2x= -a million-16 2x= -17 x= -17/2 6) -15=22x+7 -15-7=22x -22=22x x= -22/22 x= -a million

Answer 4

2^(x+3) = 2^x * 2^3 = 2^x * 8
2(x-1) = 2x-2
2^(x+3)-2(x-1) = 2^x*8-2x+2
(15/2)(2^x) = 15* (2^x / 2)
2^x / 2 = 2^(x-1)
(15/2)(2^x) = 15 * 2^(x-1)
8*2^x - 2x + 2 = 15 * 2^(x-1)
16*2^x - 4x + 4 = 15 * 2^x, since 2^(x-1) = 2^x / 2
16*2^x = 15*2^x + 4x - 4
2^x = 4x-4
The two sides are not equal

I believe that you made a typo:

2^(x+3) - 2^(x-1) = (15/2)(2^x)
2^3 * 2^x - (2^x / 2) = (15 / 2)(2^x)
Multiplying both sides with 2:
2^4 * 2^x - 2^x = 15*2^x
(2^4 - 1) * 2^x = 15*2^x
2^4 - 1 = 15
16 - 1 = 15
15 = 15
TRUE!

Answer 5

Ok, girl, here's somethin':
X is shown twice on the left, and once on the right. As soon as I tried to simplify the right, I came up with 7.5 times two raised to some power X. Remember, 2 to the power of X is 2 multiplied X times. When I got there, both sides are unequal! You don't have an equality, you have an inequality!

Answer 6

If 2^(x+3) - 2(x-1) = (15/2)(2^x) then
2^(x+3) - (15/2)(2^x) = 2(x-1)
8*(2^x) - (15/2)(2^x) = 2(x-1)
(2^x)/2 = 2(x-1)
2^x = 4(x-1). This is not true, so
the sides are not equal. Sorry pal.

Answer 7

You must be missing a ^ sign.


2^(x+3) =8*2^x

2^(x-1)= 2^x/2

2^x * (8-1/2) = 15/2 *2 ^x

Answer 8

put, x=2
2^(5)-2(1)=15(2^1)
30 =30

Answer 9

log base 2 of both sides..is this written properly?

cause i'm getting:

(x+3) - (x-1) = (15x)/2

these are clearly not equal

looks like you forgot the ^ for -2^(x-1)

Answer 10

They aren't equal the way you put them in the computer.