If 3x+10=4, what is the value of 2+5x?
The Correct Answer and Explanation is:
To solve the equation (3x + 10 = 4) and subsequently find the value of (2 + 5x), we can follow these steps:
Step 1: Solve for (x)
First, we need to isolate (x) in the equation (3x + 10 = 4). We can do this by following the order of operations, which involves eliminating the constant term on the left side of the equation.
- Subtract 10 from both sides:
[
3x + 10 – 10 = 4 – 10
]
Simplifying this gives:
[
3x = -6
] - Divide both sides by 3 to solve for (x):
[
x = \frac{-6}{3} = -2
]
Step 2: Substitute (x) into (2 + 5x)
Now that we have found (x = -2), we can substitute this value into the expression (2 + 5x):
- Calculate (5x):
[
5x = 5 \cdot (-2) = -10
] - Now substitute into the expression (2 + 5x):
[
2 + 5x = 2 + (-10) = 2 – 10 = -8
]
Conclusion
Thus, the value of (2 + 5x) is (-8).
Explanation of the Process
This problem exemplifies basic algebraic manipulation, which is a fundamental skill in mathematics. The first step of isolating the variable is critical and often involves the use of inverse operations, such as subtraction to eliminate a constant and division to solve for the variable. Once we determine the value of (x), substituting it back into another expression is straightforward but crucial for finding the final answer. The expression (2 + 5x) shows how algebra allows us to derive new information from known values, emphasizing the interconnectedness of mathematical concepts. This process underlines the importance of accuracy in each step, as errors can propagate and lead to incorrect conclusions.