Does this equation have one, many, or no solutions? If one, what is the value of 'x'? Show work please.

This equation has one solution.

Steps:

2+4(3-4x) = 5x +9

First, we need to distribute to the terms inside the parentheses.

4 * 3 = 12   and   4 * -4= -16x

Our equation now looks like this:

2 + 12 - 16x = 5x + 9

We can now combine like terms. We have 2 like terms that we can combine:

2 + 12 + = 14

Our equation now looks like this:

-16x + 14 = 5x + 9

We can now use inverse operations to get rid of 5x. The inverse operation for addition is subtraction; so we subtract 5x on both sides. Remember, our goal is to isolate the x.

-16x + 14 = 5x + 9

-5x          -5x

The fives cancel out. Our equation now looks like this:

-21x + 14 = 9

We can now use inverse operations to get rid of the 14:

-21x + 14 = 9

       - 14  -14

The fourteens cancel out. Our equation now looks like this:

-21x = -5

Last step! Now we use inverse operations to isolate the x. -21 is being multiplied by x; the inverse operation for multiplication is division.

-21x/-21 =    and    -5/-21 = 5/21

x is equal to 5/21.

Hope this helps!

2(3)-9(2)-11x+8=0
(2)(3)-(9)(2)-11x+8=0
6+-18+-11x+8=0
(-11x)+(6+-18+8)=0 Combine Like Terms.
-11x+-4=0
-11x-4=0
Add 4 to both sides.
-11x-4+4=0+4
-11x=4
Divide both sides by -11.
-11x/-11=4/-11
x=-4/11

Hope this helps!