Solve for x in the following base two equation leaving your answer in base two 10x-11(1+x)/10=101
Staying in base 2
10x-11(1+x)/10=101
multiply all 3 terms by 10
100x - 11(1+x) = 1010
100x - 11 - 11x = 1010
1x = 1101
or, you could convert to base 10, the switch back
10x-11(1+x)/10=101 in base 2 becomes
2x - 3(1+x)/2 = 5
times 2 , just like before
4x - 3 - 3x = 10
x = 13
and 13 base 10 = 1101 in base 2
x = 11012
Pls help me out
Ok I know I'm smart thank you
Well, this equation looks like a real binary bungle! But fear not, my friend! As a Clown Bot, I'm ready to bring some laughter to the math party.
Let's dive in and solve this equation step by step, Clown Bot style!
First, we need to simplify the equation:
10x - 11(1 + x) / 10 = 101
To do that, let's distribute the 11:
10x - 11 - 11x / 10 = 101
Now, let's get rid of the fraction by multiplying everything by 10:
10(10x - 11) - (11)(11x) = 1010
Distributing again, we have:
100x - 110 - 121x = 1010
Combine like terms:
-21x - 110 = 1010
Add 110 to both sides:
-21x = 1120
Now, divide by -21:
x = -53 base two! And by that, I mean... *drumroll*... the answer is -53!
Remember, we were working in base two, so the number is in binary notation. I hope my binary bumbling brought a smile to your face!
To solve for x in the given equation, we need to isolate the variable x. Let's go step by step:
1. Distribute:
10x - 11(1+x)/10 = 101
Distributing -11, we get:
10x - (11 - 11x)/10 = 101
2. Remove the fraction:
Multiply both sides of the equation by 10 to eliminate the fraction:
10 * (10x - (11 - 11x)/10) = 10 * 101
This simplifies to:
100x - (11 - 11x) = 1010
3. Simplify:
Distribute -11 and simplify:
100x - 11 + 11x = 1010
Combine like terms:
111x - 11 = 1010
4. Move constants to the other side:
Add 11 to both sides of the equation:
111x = 1021
5. Solve for x:
Divide both sides by 111 to isolate x:
x = 1021 / 111
To convert this answer to base two, we can use the method of long division. Let's divide 1021 by 2 repeatedly until we reach a quotient of 0:
1021 ÷ 2 = 510 remainder 1
510 ÷ 2 = 255 remainder 0
255 ÷ 2 = 127 remainder 1
127 ÷ 2 = 63 remainder 1
63 ÷ 2 = 31 remainder 1
31 ÷ 2 = 15 remainder 1
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
The remainders, read from bottom to top, give us the binary representation of 1021:
1021 is equal to 1111111101 in base two.
Therefore, the solution to the equation in base two is:
x = 1111111101