Question

Now that we have an equation with just one variable, x, we can perform balanced moves to try to isolate x to see if there is a value for x that will make the equation true. Since there are x terms on both sides of the equation, let’s get rid of the x term from one of the sides. What move can you make to get rid of the x term on the left side of the equation, 3x, while keeping the equation balanced?
y= 3x+6
y= 3x+3


3x+6 = 3x+3

Add 3x to each side

Multiply each side by 3x

Answer 1

To eliminate the \(3x\) term from the left side of the equation \(3x + 6 = 3x + 3\) while keeping the equation balanced, you can subtract \(3x\) from both sides. Here's how you can do it step-by-step:

1. Start with the original equation:
\[
3x + 6 = 3x + 3
\]

2. Subtract \(3x\) from both sides:
\[
3x + 6 - 3x = 3x + 3 - 3x
\]

3. This simplifies to:
\[
6 = 3
\]

This result indicates that the equation has no solution, as \(6\) does not equal \(3\). Thus, the original equation is inconsistent.

So the correct move to isolate x is to **subtract \(3x\) from both sides**. The options you provided (adding \(3x\) or multiplying both sides by \(3x\)) would not be appropriate for isolating \(x\) in this case.