Let's look at how to combine like terms to simplify equations. The balance scale shows the equation 2 s + s + 5 = 3 c. On the left side, 2 s and s are like terms because they share the same variable. We can add them together into a single term. To combine them, we add their coefficients. Thinking of s as 1 s, we add 2 + 1 to get 3 s. Our simplified equation is now 3 s + 5 = 3 c.
Let's practice with another problem. S + 3 S = 2 C + 1. First, find any like terms on the same side. On the left side, we have S and 3 S. We can combine S and 3 S. Since S is the same as 1 S, we add the coefficients 1 and 3 to get 4 S. The rewritten equation is now 4 S = 2 C + 1. In this equation, 25 C + 50 C = T + 20. Let's scan for like terms. On the left, both 25 C and 50 C have the variable C, so we can combine them. The terms on the right, T and 20, are different, so they stay as they are. To combine 25 C and 50 C, we add their coefficients. 25 + 50 is 75. So, the combined term is 75 C, making the simplified equation 75 C = T + 20.
Now look at this equation. 2X + 3X = 4 Y + Y + 2. We can only combine terms with the exact same variable. Let's simplify each side separately. Starting with the left, we add the x terms. 2x + 3x is 5x.
On the right side, we combine 4 y and y.
Thinking of y as 1 y, we add 4 and 1 to get 5 y. Our simplified equation is 5x = 5 y + 2. Let's look at one last example.
50 + 12 s + 8 s = 9 t + 6 t. This includes a constant 50 which is a number with no variable. First, let's combine the like terms on the left side. Those are 12 s and 8 s. Adding the coefficients 12 + 8 gives us 20 s. 50 is a constant with no like terms. On the right side, we combine the t terms 9 t + 6 t. Adding 9 and 6 gives us 15t. So, our fully simplified equation is 50 + 20 s = 15t. To simplify the equations, we found terms with the same variable and added their coefficients.
