What is the positive solution of x? – 36 = 5x?
The correct answer and explanation is:
We are given the equation: −36=5x-36 = 5x
Step-by-Step Solution:
To solve for xx, divide both sides of the equation by 5: x=−365x = \frac{-36}{5} x=−7.2x = -7.2
This is the only solution to the equation. However, you asked for the positive solution. Since the only solution is negative, there is no positive solution to this equation.
Final Answer:
There is no positive solution; the solution is x=−7.2x = -7.2.
Explanation (300 words):
This problem is an example of solving a simple linear equation of the form ax=bax = b, where we isolate the variable xx to find its value.
The given equation is: −36=5x-36 = 5x
This means that multiplying some number xx by 5 gives −36-36. To isolate xx, we perform the inverse operation of multiplication — that is, we divide both sides of the equation by 5. Mathematically: −365=x\frac{-36}{5} = x x=−7.2x = -7.2
This solution is unique — meaning that a linear equation with one variable typically has only one solution. The value x=−7.2x = -7.2 satisfies the equation because: 5×(−7.2)=−365 \times (-7.2) = -36
Now, it’s important to interpret the question carefully. The question asks for the positive solution of the equation. But in this case, the only solution is negative. There are no other values for xx that satisfy the equation. So, no positive value of xx can satisfy the equation −36=5x-36 = 5x.
This demonstrates an important concept in algebra: not all equations will have positive solutions, and sometimes, the nature of the equation limits the sign of the solution.