How to Solve for Y in Simple Algebraic Equations

When tackling algebraic equations, particularly those asking you to find the value of y, understanding how to isolate the variable is crucial. Many of these equations are one-step problems, typically in forms like 'number × y = answer' or 'number × y + number = answer.' Let's break down how to approach these problems step by step.

Take the equation 3y = 27 as our first example. This equation tells us that 3 times some number y equals 27. To find the value of y, we need to isolate the variable. The first step is to recognize that the operation connecting y and 3 is multiplication. To undo this multiplication, we perform the opposite operation, which is division.

Here's how you can do it: Divide both sides of the equation by 3. This gives us:

3y / 3 = 27 / 3

y = 9

Now we have solved for y, and we can conclude that in the equation 3y = 27, y equals 9.

Let’s consider another example: the equation 4y + 8 = 40. Here, we first need to isolate the term with y. To do this, we start by eliminating the constant term on the left side, which is +8. We achieve this by subtracting 8 from both sides:

4y + 8 - 8 = 40 - 8

This simplifies to:

4y = 32

Now, we see that 4 is still multiplying y. To get y alone, we divide both sides by 4:

4y / 4 = 32 / 4

y = 8

Thus, in the equation 4y + 8 = 40, y equals 8.

Understanding these basic principles not only helps you solve algebraic equations but also builds a foundation for more complex math problems in the future. These skills can be applied to real-world scenarios, such as calculating distances, budgeting, or even understanding scientific formulas. Practicing with various equations will bolster your confidence and enhance your problem-solving abilities.

If you want to practice more, try out additional problems and remember that I’m here to help you step by step. You can also explore the 'equations' section for more types of equations you might encounter in your studies.