How to Solve Linear Equations Step-by-Step: A Student's Guide
Quick Answer
To solve the equation 2x - 5 = 3(4x + 5), first apply the distributive property, then move x terms to one side, and solve for x. The solution is x = -2.
Solving linear equations is an essential skill in math that helps you understand relationships between variables. Let’s take the example equation: 2x - 5 = 3(4x + 5). Here’s how to approach it step-by-step.
### Step 1: Distributive Property
The first step involves applying the distributive property to simplify the equation. The right side of the equation is 3(4x + 5). When you distribute the 3, you multiply it by both terms inside the parentheses:
3 * 4x = 12x
3 * 5 = 15
So, the equation now reads: 2x - 5 = 12x + 15. This is a critical step because it allows you to work with simpler, combined terms.
### Step 2: Moving Variables to One Side
Next, you want to isolate the variable (x) on one side of the equation. To do this, subtract 12x from both sides:
2x - 12x - 5 = 15
This simplifies to:
-10x - 5 = 15
### Step 3: Isolating the Variable
Now, you want to isolate -10x. To do this, add 5 to both sides:
-10x = 20
### Step 4: Solving for x
Finally, divide both sides by -10 to find the value of x:
x = -2
### Conclusion
So, the solution to the equation 2x - 5 = 3(4x + 5) is x = -2.
### Real-World Application
Understanding how to solve linear equations like this one is crucial not just in math class but also in real-life situations, such as budgeting or analyzing trends. For example, if you have a budget for spending on various items, you can set up equations to see how much you can afford based on your income.
By practicing these steps, you'll gain confidence in solving similar equations. If you want to see more examples or practice problems, check the resources section on Train Your Brain!
Was this answer helpful?