Question

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Answer 1

Option A:

Hence, x ÷ 4 > x – 12 is true for x = 20.

Solution:

To find which is the suitable inequality is true for the value x = 20.

Option A: x ÷ 4 > x – 12

⇒ $\frac{x}{4}>x-12$

Multiply 4 on both sides of the inequality,

⇒ x > 4x – 48

Subtract 4x on both sides of the inequality,

⇒ –3x > – 48

⇒ 3x > 48

Divide 3 on both sides,

⇒ x > 16

If x = 20, then 20 > 16 is true.

Option B: 2x < x +22

Subtract x on both sides of the inequality,

⇒ x < 22

If x = 20, then 20 < 22 is false.

Option C: x + 30 > 3x

Subtract x on both sides of the inequality,

⇒ 30 > 2x

Divide by 2 on both sides of the inequality,

⇒ 15 > x

If x = 20, then 15 > 20 is false.

Option D: x – 5 < 2x – 35

Subtract x on both sides of the inequality,

⇒ – 5 < x – 35

Add 35 on both sides of the inequality,

⇒ 30 < x

If x = 20, then 30 < 20 is false.

Hence, x ÷ 4 > x – 12 is true for x = 20.