How to Solve Simple and Two-Step Equations in Algebra
Quick Answer
To solve simple equations like `3y = 27`, divide both sides by the coefficient of y. For two-step equations such as `5y + 15 = 65`, first subtract the constant, then divide by the coefficient.
Solving equations is a fundamental skill in algebra that can be applied in various real-life situations, from budgeting to engineering. Let's break down how to tackle both simple and two-step equations step by step.
### Understanding Simple Equations
A simple equation takes the form of `ky = a`, where `k` is a coefficient and `a` is a constant. For instance, in the equation `3y = 27`, we want to isolate `y` to find its value. The equation indicates that three times some number `y` equals 27. To solve for `y`, we perform the opposite operation of multiplication, which is division. Specifically, we divide both sides of the equation by 3:
- **Step 1:** Start with the equation: `3y = 27`
- **Step 2:** Divide both sides by 3: `y = 27 / 3`
- **Step 3:** Calculate: `y = 9`
Thus, the solution to the equation is `y = 9`.
### Moving to Two-Step Equations
Two-step equations, like `5y + 15 = 65`, require an additional step to isolate the variable. Here’s how to approach this type of equation:
- **Step 1:** Start with the equation: `5y + 15 = 65`
- **Step 2:** First, we need to eliminate the constant (15) from the left side. We do this by subtracting 15 from both sides:
`5y + 15 - 15 = 65 - 15`
This simplifies to:
`5y = 50`
- **Step 3:** Now, we divide both sides by 5 to solve for `y`:
`y = 50 / 5`
Calculating this gives:
`y = 10`
### Practice Makes Perfect
Now that you understand how to solve both simple and two-step equations, practice is essential. Try solving these problems on your own:
- **Simple Equation:** `4y = 32`
- **Two-Step Equation:** `3y + 9 = 30`
### Real-World Applications
Understanding how to solve equations is not just a math exercise; it has practical applications in daily life. For example, if you are trying to budget your monthly expenses, you might set up an equation where your total expenses equal your income. By solving the equation, you can determine how much you can spend in each category.
In summary, mastering the skills to solve both simple and two-step equations will not only help you in your algebra class but will also provide a valuable toolset for solving everyday problems. Keep practicing, and soon you will find these equations easy to manage!
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