1.5x=3 whats the answer
The Correct Answer and Explanation is :
To solve the equation (1.5x = 3), we will isolate the variable (x) by following these steps:
Step 1: Understand the equation
The equation states that one and a half times some number (x) equals three. We want to find out what that number (x) is.
Step 2: Isolate (x)
To isolate (x), we can divide both sides of the equation by (1.5):
[
x = \frac{3}{1.5}
]
Step 3: Perform the division
Now, we can perform the division:
[
x = \frac{3}{1.5} = 2
]
Thus, the solution to the equation (1.5x = 3) is (x = 2).
Explanation of the steps
- Setting up the equation: The equation (1.5x = 3) is a linear equation in one variable. It shows a direct relationship between (x) and the number 3, scaled by the factor of 1.5.
- Dividing both sides: By dividing both sides by (1.5), we are using the property of equality, which states that if two expressions are equal, then dividing both by the same non-zero number will keep them equal. This step is crucial for isolating (x).
- Understanding the result: When we calculate ( \frac{3}{1.5} ), we convert it into a more manageable form. Dividing by a decimal can be tricky, but it’s equivalent to multiplying by its reciprocal. Thus, (3 \div 1.5) can be seen as multiplying (3) by ( \frac{10}{15} ) or simplifying to ( \frac{2}{3} ), leading us back to the integer (2).
Conclusion
The solution to the equation (1.5x = 3) is (x = 2). Understanding how to manipulate equations by isolating variables is fundamental in algebra, and this example illustrates the straightforward process of solving for a variable in a linear equation.