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# List all integers satisfying the inequality -1 $$\leq$$ 2 x -6 < 4.

### Question

List all integers satisfying the inequality -1 $$\leq$$ 2 x -6 < 4.

### Options

A)
2, 3, 4, 5
B)
2, 3, 4
C)
2, 5
D)
3, 4, 5
E)
4, 5

The correct answer is B.

### Explanation:

2 $$\leq$$ 2x - 6 < 4 = 2x - 6 < 4

= 2x < 10

= x < 5

2x $$\geq$$ -2 + 6 $$\geq$$
= z $$\geq$$ 2
∴ 2 $$\leq$$ x < 5 [2, 3, 4]

## Dicussion (1)

• 2 $$\leq$$ 2x - 6 < 4 = 2x - 6 < 4

= 2x < 10

= x < 5

2x $$\geq$$ -2 + 6 $$\geq$$
= z $$\geq$$ 2
∴ 2 $$\leq$$ x < 5 [2, 3, 4]