https://file.aiquickdraw.com/mathbot/file/172589087938906et9rwq.jpg

The equation given in the image is:

\[
6.3x - 4 = 2.6x - 3
\]

Let's solve it step by step:

### Step 1: Move the variable terms to one side
Subtract \(2.6x\) from both sides:
\[
6.3x - 2.6x - 4 = 2.6x - 2.6x - 3
\]
This simplifies to:
\[
3.7x - 4 = -3
\]

### Step 2: Move the constant terms to the other side
Add 4 to both sides:
\[
3.7x - 4 + 4 = -3 + 4
\]
This simplifies to:
\[
3.7x = 1
\]

### Step 3: Solve for \(x\)
Divide both sides by 3.7:
\[
x = \frac{1}{3.7}
\]
Calculating the division:
\[
x \approx 0.27027
\]

Thus, the solution to the equation is:
\[
x \approx 0.27
\]

Would you like more details on any of the steps?

Here are 5 follow-up questions for deeper understanding:
1. What happens if you mistakenly add instead of subtract the variable terms in Step 1?
2. How would you solve this equation if there were fractions instead of decimals?
3. Can you check the solution by substituting \(x = 0.27\) back into the original equation?
4. What are the properties of equality used in each step of solving the equation?
5. How can you express this solution as a fraction instead of a decimal?

**Tip:** Always double-check your final answer by plugging it back into the original equation to verify the correctness.

Learn how to solve the linear equation 6.3x - 4 = 2.6x - 3 step by step. This problem covers key algebraic concepts like moving terms and simplifying equations. Suitable for students in Grades 8-10.

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