Let’s solve the equation for x, the number of weeks when Olivia and Addison bike the same number of miles, to confirm that it’s the same as the x-coordinate of the point of intersection. 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 right side of the equation, 10x, while keeping the equation balanced?

Question

Let’s solve the equation for x, the number of weeks when Olivia and Addison bike the same number of miles, to confirm that it’s the same as the x-coordinate of the point of intersection. 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 right side of the equation, 10x, while keeping the equation balanced?
Olivia’s miles = Addison's miles
60+20x = 90+10x

Multiply each side by 10x

Add 10x to each side

Subtract 10x from each side

GPT-4o mini · Answer

To get rid of the $10x$ term on the right side of the equation while keeping the equation balanced, you should **subtract $10x$ from each side** of the equation. So, starting with: $$ 60 + 20x = 90 + 10x $$ If you subtract $10x$ from both sides, you will have: $$ 60 + 20x - 10x = 90 + 10x - 10x $$ This simplifies to: $$ 60 + 10x = 90 $$ This is the correct move to eliminate the $10x$ term from the right side of the equation.