Question

add 6x to both sides of the equation to get rid of the −6x on the right, and get all the x terms on the left side of the equation.
y= 2x−4
x= −3y+2
x
=
−3(2x−4) + 2

x
=
−3(2x+−4) + 2

x
=
−6x + 12 + 2

x
=
−6x + 14
+
6x
+
6x

=

Answer 1

Let's start by taking it step-by-step, solving the original equation and the transformations you've outlined.

You have the equation:

1. \( y = 2x - 4 \)
2. \( x = -3y + 2 \)

Substituting the expression for \( y \) into the expression for \( x \):

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

Now, distribute \(-3\):

\[
x = -3(2x) + (-3)(-4) + 2
\]
\[
x = -6x + 12 + 2
\]
\[
x = -6x + 14
\]

Now, to get all \( x \) terms on the left side, we will add \(6x\) to both sides:

\[
x + 6x = -6x + 14 + 6x
\]

Simplifying both sides:

\[
7x = 14
\]

Dividing by \(7\):

\[
x = 2
\]

So, the result of your operation where you added \(6x\) to both sides leads us to find that \(x = 2\).