Solve the equation `15 x=21 ` and verify the result.

Options

A. `7/8`
B. `7/6`
C. `7/5`
D. `7/3`

Answer

To solve the equation \( 15x = 21 \) and verify the result, follow these steps:

### Step 1: Write down the equation
The given equation is:
\[ 15x = 21 \]

### Step 2: Isolate \( x \)
To find the value of \( x \), we need to make the coefficient of \( x \) equal to 1. We can do this by dividing both sides of the equation by 15:
\[ \frac{15x}{15} = \frac{21}{15} \]

### Step 3: Simplify the left side
The left side simplifies to:
\[ x = \frac{21}{15} \]

### Step 4: Simplify the right side
Now, we simplify \( \frac{21}{15} \) by finding the greatest common divisor (GCD) of 21 and 15, which is 3:
\[ x = \frac{21 \div 3}{15 \div 3} = \frac{7}{5} \]

### Step 5: State the solution
Thus, the value of \( x \) is:
\[ x = \frac{7}{5} \]

### Step 6: Verify the result
To verify the solution, substitute \( x = \frac{7}{5} \) back into the original equation:
\[ 15x = 21 \]
Substituting \( x \):
\[ 15 \left(\frac{7}{5}\right) = 21 \]

### Step 7: Simplify the left-hand side
Calculating the left-hand side:
\[ 15 \cdot \frac{7}{5} = \frac{15 \cdot 7}{5} = \frac{105}{5} = 21 \]

### Step 8: Compare with the right-hand side
The right-hand side of the equation is also 21:
\[ 21 = 21 \]

Since both sides are equal, the solution is verified.

### Final Answer
The solution to the equation \( 15x = 21 \) is:
\[ x = \frac{7}{5} \]