If `[5" "x" "1][{:(4),(2),(7):}]=[35]`, then x = ________.

Answer

To solve the equation given in the question, we will follow these steps:

### Step 1: Understand the matrix multiplication
We have two matrices:
1. A row matrix: \([5 \quad x \quad 1]\) (1 x 3)
2. A column matrix: \(\begin{bmatrix} 4 \\ 2 \\ 7 \end{bmatrix}\) (3 x 1)

When we multiply these matrices, the result will be a 1 x 1 matrix.

### Step 2: Set up the multiplication
Using the row-column multiplication rule, we multiply the corresponding elements and sum them up:
\[ 5 \cdot 4 + x \cdot 2 + 1 \cdot 7 = 35 \]

### Step 3: Simplify the equation
Now we simplify the left side:
\[ 20 + 2x + 7 = 35 \]

### Step 4: Combine like terms
Combine the constant terms:
\[ 27 + 2x = 35 \]

### Step 5: Isolate the variable
Subtract 27 from both sides:
\[ 2x = 35 - 27 \]
\[ 2x = 8 \]

### Step 6: Solve for x
Now divide both sides by 2:
\[ x = \frac{8}{2} = 4 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{4} \]