If`(6x - 5) = (4x + 7),` then the numerical value of `(x +1) ^(3)` is

Options

A. 216
B. 125
C. 64
D. 343

Answer

To solve the equation \( (6x - 5) = (4x + 7) \) and find the value of \( (x + 1)^3 \), we can follow these steps:

### Step 1: Set up the equation
We start with the equation:
\[ 6x - 5 = 4x + 7 \]

### Step 2: Rearrange the equation
Next, we want to isolate \( x \). We can do this by moving \( 4x \) to the left side and \( -5 \) to the right side:
\[ 6x - 4x = 7 + 5 \]

### Step 3: Simplify both sides
Now, simplify both sides:
\[ 2x = 12 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides by 2:
\[ x = \frac{12}{2} = 6 \]

### Step 5: Find \( x + 1 \)
Now that we have \( x \), we can find \( x + 1 \):
\[ x + 1 = 6 + 1 = 7 \]

### Step 6: Calculate \( (x + 1)^3 \)
Now we need to calculate \( (x + 1)^3 \):
\[ (x + 1)^3 = 7^3 \]

### Step 7: Compute \( 7^3 \)
Calculating \( 7^3 \):
\[ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 \]

Thus, the numerical value of \( (x + 1)^3 \) is:
\[ \boxed{343} \]

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