What is the value of x in the following equation?
2/3x+2=4
The Correct Answer and Explanation is:
We are asked to solve the equation:
[
\frac{2}{3}x + 2 = 4
]
Step 1: Isolate the term with ( x )
The first step is to isolate the term with ( x ) on one side of the equation. To do this, we need to remove the constant term on the left side. In this case, the constant term is ( 2 ). We can subtract ( 2 ) from both sides of the equation to maintain the equality:
[
\frac{2}{3}x + 2 – 2 = 4 – 2
]
This simplifies to:
[
\frac{2}{3}x = 2
]
Step 2: Eliminate the fraction
Next, to eliminate the fraction, we multiply both sides of the equation by the reciprocal of ( \frac{2}{3} ), which is ( \frac{3}{2} ). This step will help isolate ( x ) on the left side.
[
\frac{3}{2} \times \frac{2}{3}x = \frac{3}{2} \times 2
]
On the left side, ( \frac{3}{2} \times \frac{2}{3} = 1 ), so we are left with:
[
x = \frac{3}{2} \times 2
]
Step 3: Simplify the right side
Now, we simplify the right side of the equation:
[
x = \frac{3 \times 2}{2} = \frac{6}{2} = 3
]
Thus, the solution to the equation is:
[
x = 3
]
Step 4: Verify the solution
To verify, substitute ( x = 3 ) back into the original equation:
[
\frac{2}{3} \times 3 + 2 = 4
]
Simplifying the left side:
[
2 + 2 = 4
]
Since both sides of the equation are equal, the solution ( x = 3 ) is correct.
Conclusion
The value of ( x ) is ( 3 ). This method involves isolating the variable, eliminating fractions by multiplying by the reciprocal, and verifying the solution by substituting it back into the original equation.