Let's rearrange terms in an equation.
This balance scale represents an equation. On the left, we have a circle C, a weight of five, and two circles or 2C. On the right, we have a triangle T.
Our goal is to rewrite the equation by combining like terms. On the left, the terms with the variable C are like terms, so we can add them together. C + 2 C gives us 3 C. We can now rewrite the equation as 3 C + 5 = T.
We can change the order of terms we're adding. So C + 5 + 2 C is the same as C + 2 C + 5. Even when like terms aren't next to each other, we can always group and combine them. Let's try another. The equation is S + 3 C + S = 10. To simplify, we'll combine the like terms on the left. The terms with the variable s are like terms. Adding them gives us 2 s. The simplified equation becomes 2 s + 3 c = 10. Now let's look at this equation. 2 c = s + 2 + 2 s + 6. We have two kinds of like terms on the right side. First, let's combine the variables. We have s and 2 s which gives us 3 s. Next let's combine the constants. 2 + 6 is 8. So we can rewrite the equation as 2 c = 3 s + 8. Here's another equation. s + 2 c + 2 s + 2 c = 20. Let's combine the like terms on the left side. First we'll combine the s terms. We have S and 2 S which add up to 3 S. Next, let's combine the C terms. We have 2 C and another 2 C which gives us 4 C.
So the simplified equation is 3 S + 4 C = 20. Here we'll have to combine like terms on both sides of the equation. On the left we have 3 S + 10 + S. On the right, we have 2 C + T + C. Let's start with the left. The like terms are 3 S and S. Adding them together gives us 4 S. On the right side, the like terms are 2 C and C, which are 3 C together. So, the final simplified equation is 4 S + 10 = T + 3 C.
The main takeaway is that we can rearrange and combine variables and constants in an equation. This helps us simplify complex equations, making them easier to understand and solve.
