Find x if `7,9,84,` x are in proportion

Answer

To find the value of \( x \) in the proportion \( 7, 9, 84, x \), we can follow these steps:

### Step 1: Understand the Proportion
The numbers \( 7, 9, 84, x \) are in proportion. This means that the ratio of the first two numbers is equal to the ratio of the last two numbers. We can express this as:

\[ \frac{7}{9} = \frac{84}{x} \]

### Step 2: Cross Multiply
To eliminate the fractions, we will cross multiply:

\[ 7 \cdot x = 9 \cdot 84 \]

### Step 3: Calculate \( 9 \cdot 84 \)
Now, we calculate \( 9 \cdot 84 \):

\[ 9 \cdot 84 = 756 \]

### Step 4: Substitute Back
Now we substitute this back into our equation:

\[ 7x = 756 \]

### Step 5: Solve for \( x \)
To find \( x \), we divide both sides by 7:

\[ x = \frac{756}{7} \]

### Step 6: Perform the Division
Now we perform the division:

\[ 756 \div 7 = 108 \]

### Final Answer
Thus, the value of \( x \) is:

\[ x = 108 \]