If `x` satisfies the inequations `2x-7lt11` and `3x+4lt-5,` then `x` lies in the interval `(-oo,-m)`. The value of 'm' is

Options

A. `2`
B. `3`
C. `4`
D. `5`

Answer

To solve the given inequalities \(2x - 7 < 11\) and \(3x + 4 < -5\) step by step, we will follow these steps:

### Step 1: Solve the first inequality \(2x - 7 < 11\)

1. **Add 7 to both sides**:
\[ 2x < 11 + 7 \]
\[ 2x < 18 \]

2. **Divide both sides by 2**:
\[ x < \frac{18}{2} \]
\[ x < 9 \]

### Step 2: Solve the second inequality \(3x + 4 < -5\)

1. **Subtract 4 from both sides**:
\[ 3x < -5 - 4 \]
\[ 3x < -9 \]

2. **Divide both sides by 3**:
\[ x < \frac{-9}{3} \]
\[ x < -3 \]

### Step 3: Combine the results

From the first inequality, we have:
\[ x < 9 \]
From the second inequality, we have:
\[ x < -3 \]

### Step 4: Determine the interval for \(x\)

Since \(x\) must satisfy both inequalities, we take the more restrictive condition:
\[ x < -3 \]

Thus, the solution for \(x\) lies in the interval:
\[ (-\infty, -3) \]

### Step 5: Identify the value of \(m\)

The problem states that \(x\) lies in the interval \((-∞, -m)\). From our solution, we see that:
\[ -m = -3 \]

Therefore, solving for \(m\):
\[ m = 3 \]

### Final Answer:
The value of \(m\) is \(3\).

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