Question

Solve for the variable:



`9x\ +\ 20\ +\ 2\left(3x\ -\ 4\right)\ =\ -2\left(4\ -\ 6x\right)`

Answer 1

Let's solve the equation step by step:

Given equation:

\[
9x + 20 + 2(3x - 4) = -2(4 - 6x)
\]

First, we distribute the terms on both sides.

For the left side, distribute \(2\) inside the parentheses:

\[
2(3x - 4) = 6x - 8
\]

Now substitute this back into the equation:

\[
9x + 20 + 6x - 8 = -2(4 - 6x)
\]

Next, simplify the left side:

\[
(9x + 6x) + (20 - 8) = 15x + 12
\]

Now, for the right side, distribute \(-2\):

\[
-2(4) + (-2)(-6x) = -8 + 12x
\]

Now we have:

\[
15x + 12 = 12x - 8
\]

Next, let's isolate \(x\) by moving all \(x\) terms to one side and constant terms to the other side. First, subtract \(12x\) from both sides:

\[
15x - 12x + 12 = -8
\]

This simplifies to:

\[
3x + 12 = -8
\]

Now, subtract \(12\) from both sides:

\[
3x = -8 - 12
\]

This simplifies to:

\[
3x = -20
\]

Finally, divide both sides by \(3\):

\[
x = -\frac{20}{3}
\]

Thus, the solution for \(x\) is:

\[
\boxed{-\frac{20}{3}}
\]