Let's solve the equation \( 1 - 2x + 5 = 4x - 3 \).

### Step 1: Combine like terms on each side
First, simplify both sides of the equation by combining like terms.

On the left-hand side:
\[
1 + 5 - 2x = 6 - 2x
\]

So the equation becomes:
\[
6 - 2x = 4x - 3
\]

### Step 2: Move all terms involving \(x\) to one side
Next, add \(2x\) to both sides to move all \(x\)-terms to the right side:
\[
6 = 6x - 3
\]

### Step 3: Move constant terms to the other side
Add 3 to both sides to isolate the term with \(x\):
\[
9 = 6x
\]

### Step 4: Solve for \(x\)
Divide both sides by 6 to solve for \(x\):
\[
x = \frac{9}{6} = \frac{3}{2}
\]

So, the solution is \( x = \frac{3}{2} \).

Would you like more details or have any questions?

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**Related Questions:**
1. How do you solve equations with variables on both sides?
2. What are the steps to combine like terms?
3. How can you check if your solution is correct?
4. What happens if you subtract variables instead of adding them?
5. How do you solve an equation when \(x\) is a fraction?

**Tip:** Always keep track of the signs (positive or negative) while moving terms from one side of the equation to the other to avoid mistakes.

Learn how to solve the equation 1 - 2x + 5 = 4x - 3 with detailed step-by-step instructions. This problem covers solving linear equations with variables on both sides, suitable for Grades 7-9.

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