The inequality `-1le2x+4lt5`, where x is an integer can be represented on the number line as:

Options

A.
B.
C.
D.

Answer

To solve the inequality \(-1 \leq 2x + 4 < 5\) where \(x\) is an integer, we will break it down into steps.

### Step 1: Split the Compound Inequality
We can rewrite the compound inequality as two separate inequalities:
1. \(2x + 4 \geq -1\)
2. \(2x + 4 < 5\)

### Step 2: Solve the First Inequality
Starting with the first inequality:
\[ 2x + 4 \geq -1 \]
Subtract 4 from both sides:
\[ 2x \geq -1 - 4 \]
\[ 2x \geq -5 \]
Now, divide both sides by 2:
\[ x \geq -\frac{5}{2} \]
This simplifies to:
\[ x \geq -2.5 \]

### Step 3: Solve the Second Inequality
Now, we solve the second inequality:
\[ 2x + 4 < 5 \]
Subtract 4 from both sides:
\[ 2x < 5 - 4 \]
\[ 2x < 1 \]
Now, divide both sides by 2:
\[ x < \frac{1}{2} \]

### Step 4: Combine the Results
Now we have two inequalities:
1. \(x \geq -2.5\)
2. \(x < 0.5\)

### Step 5: Determine Integer Solutions
Since \(x\) must be an integer, we consider the integers that satisfy both inequalities:
- The integers greater than or equal to \(-2.5\) are \(-2, -1, 0\).
- The integers less than \(0.5\) are \(-2, -1, 0\).

Thus, the integer solutions are:
\[ x = -2, -1, 0 \]

### Step 6: Represent on the Number Line
On the number line, we would represent the integers \(-2\), \(-1\), and \(0\) as points marked on the line.

### Final Answer
The integer solutions to the inequality \(-1 \leq 2x + 4 < 5\) are \(-2\), \(-1\), and \(0\).

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