How do i solve this X/3+10=15
The Correct Answer and Explanation is :
The correct answer is: X = 15
To solve the equation ( \frac{X}{3} + 10 = 15 ), we can follow these steps:
- Isolate the Fraction: Start by isolating the term that contains the variable (X). To do this, subtract 10 from both sides of the equation: [
\frac{X}{3} + 10 – 10 = 15 – 10
] Simplifying both sides gives: [
\frac{X}{3} = 5
] - Eliminate the Fraction: Now, we want to eliminate the fraction to solve for (X). We can do this by multiplying both sides of the equation by 3: [
3 \cdot \frac{X}{3} = 3 \cdot 5
] The left side simplifies to (X) (since (3) in the numerator and denominator cancels out), while the right side becomes: [
X = 15
] - Final Solution: Thus, the solution to the equation ( \frac{X}{3} + 10 = 15 ) is: [
X = 15
]
Explanation
In algebra, solving equations involves isolating the variable (in this case, (X)) through a series of mathematical operations. The first step typically involves removing constants from the side of the equation that contains the variable. Here, we subtracted 10 to get (\frac{X}{3}) by itself.
Next, we focused on getting rid of the fraction, which is often necessary for clearer calculations. By multiplying both sides by 3, we effectively returned to a simpler form of the equation, revealing the value of (X).
This process exemplifies a fundamental principle in algebra known as the “balance method,” which states that whatever you do to one side of the equation must also be done to the other to maintain equality.
The final result of (X = 15) not only solves the original equation but also demonstrates the logical progression of isolating the variable through careful, step-by-step manipulation of the equation.