Solving Equations After Combining Like Terms

Let's see how to solve equations by simplifying them using different methods. This equation is a + 5 + 2 a = 35. Before we solve for a, it helps to simplify by combining like terms. Here we have a and 2 a. So a + 2 a gives us 3 a. Our simplified equation is 3 a + 5 = 35. To solve for a, we need to isolate it. First, let's subtract 5 from both sides. 35 - 5 is 30. So now 3 a = 30. We can divide both sides by 3, which gives us a = 10.

Let's look at another one. 2x + 8 + 6 x + 2 = 26. We have two sets of like terms to combine, the x terms and the constant numbers. Let's start with the constants 8 and 2. 8 + 2 is 10. Next, the x terms.

2x + 6x = 8x. Our simplified equation is 8x + 10 = 26. Now, we can solve for x by subtracting 10 from both sides. 26 - 10 is 16. That leaves us with 8x = 16. To find a single x, we divide both sides by 8. 16 / 8 is 2. So, x = 2.

This equation is 3 y + 30 = 90. We can use factoring to simplify the equation.

Factoring means pulling out a common factor. Here both 3 y and 30 are divisible by 3. So we pull the three outside a set of parenthesis. Inside we divide each original term by 3. 3 y / 3 leaves y and 30 / 3 gives us 10. The factored equation is 3 * the quantity y + 10 = 90.

To solve this, let's divide both sides by 3. On the left, we're left with y + 10. On the right, 90 / 3 is 30. This gives us y + 10 = 30. Now, we can subtract 10 from both sides to find that y equals 20.

We've seen how combining like terms and factoring help simplify equations, making them easier to solve.