if `7-2k le 3`, what si the least possible value of 2k+7?

Options

A. `-3`
B. 10
C. 11
D. 13

Answer

To solve the inequality \( 7 - 2k \leq 3 \) and find the least possible value of \( 2k + 7 \), we can follow these steps:

### Step 1: Solve the inequality
Start with the given inequality:
\[ 7 - 2k \leq 3 \]

### Step 2: Isolate the term involving \( k \)
Subtract 7 from both sides:
\[ -2k \leq 3 - 7 \]
This simplifies to:
\[ -2k \leq -4 \]

### Step 3: Divide by -2
When dividing by a negative number, remember to flip the inequality sign:
\[ k \geq 2 \]

### Step 4: Find the expression \( 2k + 7 \)
We need to find the least value of \( 2k + 7 \). Substitute \( k \) with the minimum value from the inequality:
\[ 2k + 7 = 2(2) + 7 \]

### Step 5: Calculate the value
Now calculate:
\[ 2(2) + 7 = 4 + 7 = 11 \]

### Conclusion
Thus, the least possible value of \( 2k + 7 \) is:
\[ \boxed{11} \]

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