Which equation has x=4 as the solution?
The correct answer and explanation is :
To identify an equation with ( x = 4 ) as the solution, let’s first understand the concept of a solution to an equation. A solution to an equation is the value of ( x ) that makes the equation true. For example, if we have the equation:
[
2x + 3 = 11
]
We can solve for ( x ) as follows:
- Subtract 3 from both sides:
[
2x = 11 – 3
]
[
2x = 8
] - Divide both sides by 2:
[
x = \frac{8}{2} = 4
]
Thus, ( x = 4 ) is the solution to the equation ( 2x + 3 = 11 ).
Explanation
To make sure that ( x = 4 ) is the solution to any given equation, we can substitute ( x = 4 ) into the equation and verify if both sides are equal. In the case of the equation ( 2x + 3 = 11 ):
Substituting ( x = 4 ):
[
2(4) + 3 = 8 + 3 = 11
]
This confirms that the equation holds true when ( x = 4 ), so ( x = 4 ) is indeed a solution.
Other equations that have ( x = 4 ) as the solution could look like:
- ( 3x – 8 = 4 ) Solving this: Add 8 to both sides:
[
3x = 4 + 8 = 12
] Divide by 3:
[
x = \frac{12}{3} = 4
] - ( \frac{x}{2} + 1 = 3 ) Subtract 1 from both sides:
[
\frac{x}{2} = 3 – 1 = 2
] Multiply both sides by 2:
[
x = 4
]
In conclusion, there are many different types of equations that can have ( x = 4 ) as the solution, and solving each of these equations involves isolating ( x ) and verifying that it satisfies the equation.