Question

1) The solution set of x < 5 and x > equal 2 is____​
2) The solution set of |x-1| less than eual to -1 =____
3) If ( n/8) = (n/6) ,find n.

Answer 1

Answer:

1) {2,3,4}

2) {-1}

3) {2}

Answer 2

Answer:

1. The required solution set is { 2, 3, 4 }.

2. The required solution set is { }.

3. The value of n is 0.

Step-by-step-explanation:

1.

The given inequalities are x < 5 and x ≧ 2.

∴ 5 > x ≧ 2

2 ≦ x < 5

∴ x ∈ [ 2, 5 )

∴ The required solution set is { 2, 3, 4 }.

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2.

The given inequality is | x - 1 | ≦ - 1.

| x - 1 | ≦ - 1

⇒ x - 1 ≦ - 1 OR x - 1 ≧ 1

⇒ x ≦ - 1 + 1 OR x ≧ 1 + 1

⇒ x ≦ 0 OR x ≧ 2

⇒ x ∈ ( - ∞, 0 ] OR x ∈ [ 2, ∞ )

The two sets don't have any common number. So, there is no number such that less than or equal to 0 and simultaneously greater than or equal to 2.

∴ The solution set of given inequality is { }.

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3.

The given equation is

n / 8 = n / 6

⇒ 6n = 8n

⇒ 8n - 6n = 0

⇒ 2n = 0

⇒ n = 0 / 2

⇒ n = 0

∴ The value of n is 0.