To solve the equation 1x + 3x + 10x + 2 = 0, we first need to combine like terms.
1. **Combine like terms:**
The terms with ‘x’ are 1x, 3x, and 10x. Adding these together, we have:
1x + 3x + 10x = 14x
2. **Rewrite the equation:**
Now, we can rewrite our equation as:
14x + 2 = 0
3. **Isolate x:**
Next, we can isolate ‘x’ by moving 2 to the other side:
14x = -2
4. **Solve for x:**
Now, divide both sides by 14:
x = -2/14
You can simplify this to:
x = -1/7
5. **Check your solution:**
To verify the solution, substitute x = -1/7 back into the original equation:
1(-1/7) + 3(-1/7) + 10(-1/7) + 2 = 0
This simplifies to:
-1/7 – 3/7 – 10/7 + 2 = 0
Combine the fractions:
-14/7 + 2 = 0
Since 2 = 14/7, we can rewrite:
-14/7 + 14/7 = 0
Thus, confirming that our solution is correct!
6. **Conclusion:**
After solving, the only value we found for ‘x’ is:
x = -1/7
Since there’s only one solution, if we were to order solutions from least to greatest, we simply have:
x = -1/7
Thus, the final answer is -1/7.