2x+3=10
The correct answer and explanation is:
To solve the equation 2x+3=102x + 3 = 10, the goal is to isolate the variable xx.
Step-by-Step Solution:
- Start with the given equation: 2x+3=102x + 3 = 10
- Subtract 3 from both sides of the equation:
The purpose of this step is to eliminate the constant term (3) on the left side. 2x=10−32x = 10 – 3 This simplifies to: 2x=72x = 7 - Divide both sides by 2:
To isolate xx, divide both sides of the equation by 2. 2×2=72\frac{2x}{2} = \frac{7}{2} This simplifies to: x=72x = \frac{7}{2} Or equivalently, x=3.5x = 3.5
Final Answer:
The solution to the equation is x=3.5x = 3.5.
Explanation:
The equation 2x+3=102x + 3 = 10 is a linear equation, meaning it involves a straight-line relationship between the variable and constants. The process of solving linear equations generally involves isolating the variable on one side of the equation.
In this case, the first step is to remove the constant term from the left side of the equation by subtracting 3 from both sides. After simplifying the equation to 2x=72x = 7, the next step is to isolate xx by dividing both sides of the equation by the coefficient of xx, which is 2. This results in the solution x=3.5x = 3.5.
Understanding how to manipulate equations in this way is fundamental for solving algebraic problems and is essential for many areas of mathematics. Solving linear equations is a foundational skill, as it applies to solving for unknowns in more complex equations and real-world scenarios.