The mean of the following numbers is 7.Find the value of x. What is infinedian, mode and the range? x+2 12, 3x+1 9

## Step 1: Calculate the sum of the given numbers<br />### The given numbers are $x+2$, 12, $3x+1$, and 9. Their sum is $(x+2) + 12 + (3x+1) + 9 = 4x + 24$.<br /><br />## Step 2: Calculate the value of x<br />### The mean of the numbers is 7, and there are 4 numbers. Therefore, the sum of the numbers divided by 4 equals 7. So, $\frac{4x + 24}{4} = 7$. Multiplying both sides by 4 gives $4x + 24 = 28$. Subtracting 24 from both sides gives $4x = 4$. Dividing both sides by 4 gives $x = 1$.<br /><br />## Step 3: Substitute x and order the numbers<br />### Substituting $x=1$ into the expressions gives the numbers: $1+2=3$, 12, $3(1)+1=4$, 9. Ordering these from least to greatest gives: 3, 4, 9, 12.<br /><br />## Step 4: Calculate the median<br />### The median is the middle value. Since there are four numbers, the median is the average of the two middle numbers: $\frac{4+9}{2} = \frac{13}{2} = 6.5$.<br /><br />## Step 5: Calculate the mode<br />### The mode is the number that appears most frequently. Since all numbers appear only once, there is no mode.<br /><br />## Step 6: Calculate the range<br />### The range is the difference between the largest and smallest numbers: $12 - 3 = 9$.