An algebra question?

Question

The professor didn't cover this type of problem...I could use some step-by-step help solving this problem.

6[x-(2x+3)]=8-5x

And I really suck at fractions...

7/2x+1 - 8x/2x-1= -4
seven over two X plus one minus eight X over two X minus one

Answer 1

1) Collect similar terms and distribute where appropriate:

6(x - (2x + 3)) = 8 - 5x

6(x - 2x - 3) = 8 - 5x

6(-x - 3) = 8 - 5x

-6x - 18 = 8 - 5x

-18 = 8 + x

x = -26

Edit: Corrected lost minus sign. Thanks, enthalpy man.

2) I assume the binomials are the denominators:

7/(2x + 1) - 8x/(2x - 1) = -4

First thing to note: you are not allowed to divide by zero, so any value that makes either 2x + 1 or 2x - 1 equal zero is disallowed. Your solution cannot include either 1/2 or -1/2, therefore.

Now: Mulitply through by the least common denominator to clear the fractions. The LCD will be (2x + 1)(2x - 1), and the result will be

7(2x - 1) - 8x(2x + 1) = -4(2x + 1)(2x - 1)

14x - 7 - 16x^2 - 8x = -4(4x^2 - 1)

14x - 7 - 16x^2 = -16x^2 + 4

Note that the -16x^2 cancels, so you're left with

14x - 7 = 4

and you should be able to solve that.

Answer 2

6[x-(2x+3)]=8-5x

Okay lets break it down and work on the left side first.
6[x-(2x+3)] Original Left Side
6(x-2x-3) Distribute the minus sign
6(-x-3) Combine the x terms
-6x-18 Distribute the 6

8-5x Original Right Side of the equation
-6x-18 = 8-5x Simplified lef side and original right side
-x-18=8 Move 5x to the other side
-x = 26 Move 18 to the right side
x = -26 Divide each side by -1

Now for the next problem...
7/2x+1 - 8x/2x-1= -4

First you should multiply everything by 2 to get rid of the yucky fractions. So the equation then becomes...

7x + 2 - 8x - 2 = -8
-x = -8 Combine the x terms and the 2s cancel each other out
x=8 Divide each side by -1
YOU ARE DONE!!! :-)

Answer 3

What you want to do is to remove the parentheses and brackets by working your way inside out. The parentheses are removed by multiplying each term by -1
6[x - 2x - 3] = 8 - 5x
Collect like terms in the bracket to get...
6[-x - 3] = 8 - 5x
Use the distributive property to remove the brackets...
-6x - 18 = 8 - 5x
Solve the equation by getting the x terms to the left and the constant terms to the right...
-1x = 26
Divide by -1 to get...
x = -26

For the second one, you want to clear out the fraction by multiplying through by the LCD of (2x+1)(2x - 1)
This will give us...
7(2x - 1) - 8x(2x + 1) = -4(2x + 1)(2x - 1)
Mutiply this out to get...
14x - 7 - 16x^2 - 8x = -16x^2 + 4
Collect like terms to get...
-16x^2 + 6x - 7 = -16x^2 + 4
Get the x's to one side and the constants on the other side...
6x = 11
x = 11/6

Answer 4

Here goes

6[x-(2x+3)]=8-5x

we will get rid of the brackets first

6[x-2x-3]=8-5x

then multiply it out

6x-12x-18=8-5x

now simplify

-6x + 5x = 8 +18 ( I took all the X's to one side and all the numbers to the other side)

-x=26

x=-26 this is your answer

now I think the next one is like this

7/(2x+1) - 8x/(2x-1)= -4

so in this case we will get rid of the fractions first
and in order to do this you have to multiply both sides by

(2x+1)(2x-1) and you get

7(2x-1)-8x(2x+1)=-4(2x+1)(2x-1)

14x-7-16x^2-8x=-4(4x^2+2x-2x-1)

6x-7-16x^2 = -16x^2+4

14x=11

x=11/14

Answer 5

6[x-(2x+3)]=8-5x
first thing I would do is to distribute the 6
6x-6(2x+3)=8-5x
6x-12x-18 =8-5x
now you have everything in simple terms, so combine like terms.
-6x -18= 8-5x
get all the x's on one side, and the number terms on the other side.
-1x -18=8
-x = 26
x= -26

7/(2x+1) - 8x/(2x-1) = -4
you need to get a common denominator
[7(2x-1)] / [(2x+1)(2x-1)] - [8x(2x+1)] / [(2x-1)(2x+1)] = [-4(2x-1)(2x+1)] / [(2x-1)(2x+1)]
now you can combine the 2 terms on the left side of the equation.
( [7(2x-1)]-[8x(2x+1)] ) / [(2x-1)(2x+1)] = [-4(2x-1)(2x+1)] / [(2x-1)(2x+1)]
Now that you have it in the form something/x = somethingelse/x, you can drop the denominator
( [7(2x-1)]-[8x(2x+1)] ) = [-4(2x-1)(2x+1)]
distribute(dont forget your negatives!)..
[(14x-7)-(16x^2 +8x)] = [-4(2x-1)(2x+1)]
[14x-7-16x^2 -8x] = [-4 (4x^2 -1)]
14x-7-16x^2 -8x = -16x^2 +4
notice, you have a -16x^2 on both sides of the equation, so they cancel each other out.
14x-7 -8x = 4
combine like terms..
6x = 11
x= 11/6
go back and check it in the original equation to see if it works. It does, so it is the correct solution.

ALWAYS DOUBLE CHECK ANSWERS. :-)

Answer 6

For increasing cubic binomials the regular formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 7

6x-(12x+18)=8-5x
6x-12x=22 6x=34
x=5.repeating 6
note- i have no idea how i did that

Answer 8

well first of all you have to follow the order of operations, which is parenthesis first, exponents second, multiplication third, divicion fourth, addition fifth, and subtraction sixth.

hope that helps.

Answer 9

6(x-(2x+3))=8-5x
6(x-2x-3)=8-5x
6(-x-3)=8-5x
-6x-18=8-5x
-x=26
x=-26
i think this is right! hope it helps!