If `3 le 3t-18 le 18` then which one of the following is true

Options

A. `15 le 2t+1 le 20`
B. `8 le t le 12`
C. `8 le t + 1 le 13`
D. `21 le 3t le 24`

Answer

To solve the inequality \(3 \leq 3t - 18 \leq 18\), we will break it down into two parts and solve each part step by step.

### Step 1: Break down the compound inequality
We can rewrite the compound inequality as two separate inequalities:
1. \(3 \leq 3t - 18\)
2. \(3t - 18 \leq 18\)

### Step 2: Solve the first inequality
Starting with the first inequality:
\[ 3 \leq 3t - 18 \]
Add 18 to both sides:
\[ 3 + 18 \leq 3t \]
This simplifies to:
\[ 21 \leq 3t \]
Now, divide both sides by 3:
\[ 7 \leq t \]
or
\[ t \geq 7 \]

### Step 3: Solve the second inequality
Now, let's solve the second inequality:
\[ 3t - 18 \leq 18 \]
Add 18 to both sides:
\[ 3t \leq 18 + 18 \]
This simplifies to:
\[ 3t \leq 36 \]
Now, divide both sides by 3:
\[ t \leq 12 \]

### Step 4: Combine the results
From the two inequalities we have:
1. \(t \geq 7\)
2. \(t \leq 12\)

Combining these results, we find:
\[ 7 \leq t \leq 12 \]

### Conclusion
Thus, the solution to the inequality \(3 \leq 3t - 18 \leq 18\) is:
\[ t \in [7, 12] \]