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?

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

GPT-4o mini · Answer

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.