Simplifying Equations by Combining Like Terms

Let's look at solving equations by combining like terms. We'll simplify equations by grouping constants and variables. Here's our first equation. 2 C + 8 + 12 = 30. On the left side, we have two constant terms, 8 and 12. Let's combine these like terms. Adding 8 + 12 gives us 20. So, the simplified equation is 2 C + 20 = 30.

Now, let's solve for C. First subtract 20 from both sides. 30 - 20 is 10. This leaves us with 2 C = 10.

If 2 C = 10, we can find C by dividing by 2. So C = 5.

Let's try another one. The equation is 15 = 2 S + S + 9 + 3. On the right side, there are two S terms and two constant terms.

Let's combine the constants first. 9 + 3 is 12. Now, let's combine the variables.

Remember, s is the same as 1 s. So, 2 s + s is 3 s. The simplified equation is 15 = 3 s + 12. When an equation has multiple constants or terms with the same variable, we call them like terms.

Combining them is often the first step to solving the equation. Now let's find the solution for 15 = 3 s + 12. To isolate 3s, subtract 12 from both sides.

15 - 12 is 3. That leaves us with 3 = 3 s. If 3 = 3, then s = 1.

Here we need to combine like terms on both sides. On the left side 1 + 9 is 10 and 2 c + 2 c is 4 c.

On the right side, 7 + 11 is 18. So, the simplified equation is 10 + 4 C = 18.

Now, let's solve for C. First, subtract 10 from both sides. 18 - 10 is 8. That leaves 4 C= 8. If 4 C= 8, divide both sides by 4 to find that C equals 2.

Combining like terms is a key first step that helps simplify equations, making them easier to solve.