IF `4x+2y=24` and `(7y)/(2x)=7`, what is the value of x?

Answer

To solve the equations \(4x + 2y = 24\) and \(\frac{7y}{2x} = 7\) to find the value of \(x\), we can follow these steps:

### Step 1: Simplify the second equation
The second equation is given as:
\[ \frac{7y}{2x} = 7 \]
To simplify, we can multiply both sides by \(2x\) to eliminate the fraction:
\[ 7y = 14x \]
Now, we can divide both sides by 7:
\[ y = 2x \]

**Hint:** To eliminate a fraction, multiply both sides of the equation by the denominator.

### Step 2: Substitute \(y\) in the first equation
Now that we have \(y = 2x\), we can substitute this expression for \(y\) into the first equation:
\[ 4x + 2(2x) = 24 \]
This simplifies to:
\[ 4x + 4x = 24 \]

**Hint:** When substituting, make sure to distribute correctly if there are coefficients.

### Step 3: Combine like terms
Combine the terms on the left side of the equation:
\[ 8x = 24 \]

**Hint:** Combining like terms involves adding or subtracting coefficients of the same variable.

### Step 4: Solve for \(x\)
Now, divide both sides by 8 to isolate \(x\):
\[ x = \frac{24}{8} = 3 \]

**Hint:** To isolate a variable, perform the inverse operation (in this case, division).

### Final Answer
The value of \(x\) is:
\[ \boxed{3} \]