Have you ever been puzzled by a linear equation like 4.8 + 6.3x = 4.18 + 58.56x, wondering how to solve for x? If so, this blog post is the perfect guide for you! We’ll delve into the world of linear equations, providing step-by-step instructions on how to tackle and solve even the most challenging equations like this one.

Solving linear equations can often seem daunting, especially when dealing with complex numbers and multiple variables. However, by following a systematic approach and understanding the underlying principles, you can conquer any linear equation that comes your way.

The key to solving linear equations is to isolate the variable you want to solve for on one side of the equation and all the constant terms on the other side. This allows you to simplify the equation and find the value of the variable.

To solve the given equation 4.8 + 6.3x = 4.18 + 58.56x, follow these steps:

- Gather like terms by subtracting 4.18 from both sides of the equation.
- Combine like terms: 0.62 + 52.26x = 58.56x.
- Subtract 52.26x from both sides to get -51.64x = -0.62.
- Divide both sides by -51.64 to solve for x: x = 0.012.

In conclusion, solving linear equations requires a methodical approach and an understanding of the underlying principles. By following the steps outlined in this blog post, you’ll be able to tackle even the most challenging linear equations with confidence, empowering you to solve a wide range of problems with ease.

**Solving the Linear Equation: 4.8 – 6.3x + 4.18 = 58.56x**

**Introduction**

A linear equation is a mathematical equation that represents a straight line when its variables are plotted on a graph. In this article, we will be solving the linear equation 4.8 – 6.3x + 4.18 = 58.56x for the variable x.

**Step 1: Combining Like Terms**

The first step in solving the equation is to combine like terms on both sides of the equation. Like terms are terms that contain the same variable raised to the same power. In this case, the like terms are 4.8 and 4.18, and -6.3x and 58.56x.

4.8 – 6.3x + 4.18 = 58.56x

4.8 + 4.18 – 6.3x = 58.56x

**Step 2: Simplifying the Equation**

Next, we simplify the equation by adding the like terms on both sides.

9 – 6.3x = 58.56x

**Step 3: Isolating the Variable**

The next step is to isolate the variable x on one side of the equation. To do this, we add 6.3x to both sides of the equation.

9 – 6.3x + 6.3x = 58.56x + 6.3x

9 = 64.86x

**Step 4: Solving for x**

Finally, we solve for x by dividing both sides of the equation by 64.86.

9/64.86 = x

x = 0.1387

**Conclusion**

Therefore, the solution to the linear equation 4.8 – 6.3x + 4.18 = 58.56x is x = 0.1387. This means that when x is equal to 0.1387, the equation will be true.

**FAQs**

**1. What is a linear equation?**

A linear equation is a mathematical equation that represents a straight line when its variables are plotted on a graph.

**2. What are like terms?**

Like terms are terms that contain the same variable raised to the same power.

**3. How do you solve a linear equation?**

To solve a linear equation, you need to isolate the variable on one side of the equation. To do this, you can add, subtract, multiply, or divide both sides of the equation by the same value.

**4. What is the solution to the equation 4.8 – 6.3x + 4.18 = 58.56x?**

The solution to the equation 4.8 – 6.3x + 4.18 = 58.56x is x = 0.1387.

**5. Can you provide an example of a linear equation?**

Yes, an example of a linear equation is y = 2x + 3. This equation represents a straight line with a slope of 2 and a y-intercept of 3.

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