How to solve the equation –3x + 1 + 10x = x + 4

Question

Emily Rosen · Accepted Answer

The solution to the equation $-3x + 1 + 10x = x + 4$ is $ x = \frac{1}{2} $.

Emily Rosen · Accepted Answer

### Step 1: Combine Like Terms

Start by simplifying the left side of the equation:

$$
-3x + 10x + 1 = x + 4
$$

Combine like terms:

$$
( -3x + 10x ) + 1 = x + 4
$$

This simplifies to:

$$
7x + 1 = x + 4
$$

### Step 2: Move Variables to One Side

Next, we need to isolate the variable $ x $. To do this, subtract $ x $ from both sides of the equation:

$$
7x + 1 - x = x + 4 - x
$$

This simplifies to:

$$
6x + 1 = 4
$$

### Step 3: Isolate the Variable

Subtract 1 from both sides to move the constant term to the right side:

$$
6x + 1 - 1 = 4 - 1
$$

This simplifies to:

$$
6x = 3
$$

### Step 4: Solve for $ x $

Finally, divide both sides by 6 to solve for $ x $:

$$
\frac{6x}{6} = \frac{3}{6}
$$

This results in:

$$
x = \frac{1}{2}
$$

### Conclusion

**The solution to the equation is $ x = \frac{1}{2} $.**

Explanation