One experessing x in terms of y for the linear equation `2/3x+4y=-7` which of the following is correct

Options

A. `y=(-21-12x)/2`
B. `x=(-21-12y)/2`
C. `y=-7+2/3x`
D. `x=-7+4y`

Answer

To express \( x \) in terms of \( y \) for the equation \( \frac{2}{3}x + 4y = -7 \), we will follow these steps:

### Step 1: Isolate the term containing \( x \)
Start with the original equation:
\[ \frac{2}{3}x + 4y = -7 \]
To isolate the term containing \( x \), subtract \( 4y \) from both sides:
\[ \frac{2}{3}x = -7 - 4y \]

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by \( 3 \):
\[ 3 \cdot \frac{2}{3}x = 3(-7 - 4y) \]
This simplifies to:
\[ 2x = -21 - 12y \]

### Step 3: Solve for \( x \)
Now, divide both sides by \( 2 \) to solve for \( x \):
\[ x = \frac{-21 - 12y}{2} \]
This can be simplified further:
\[ x = -\frac{21}{2} - 6y \]

### Final Expression
Thus, the expression for \( x \) in terms of \( y \) is:
\[ x = -\frac{21}{2} - 6y \]