Question

What is the value of x that makes this equation true?
-5 (2x - 3) + 4x = -3x + 6

Answer 1

To solve the equation \(-5 (2x - 3) + 4x = -3x + 6\), we will first distribute the \(-5\) on the left side.

Starting with the left side:

\[
-5 (2x - 3) = -5 \cdot 2x + (-5) \cdot (-3) = -10x + 15
\]

Now, we can rewrite the equation:

\[
-10x + 15 + 4x = -3x + 6
\]

Next, we combine like terms on the left side:

\[
(-10x + 4x) + 15 = -3x + 6
\]

This simplifies to:

\[
-6x + 15 = -3x + 6
\]

Now, we isolate the \(x\) terms by adding \(6x\) to both sides of the equation:

\[
15 = 3x + 6
\]

Next, we isolate the constant term by subtracting \(6\) from both sides:

\[
15 - 6 = 3x
\]

This simplifies to:

\[
9 = 3x
\]

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

\[
x = 3
\]

Thus, the value of \(x\) that makes the equation true is:

\[
\boxed{3}
\]