14 Niluka thinks of an integer. He multiplies it by 6 and subtracts 20 . He multiplies the answer by 2 and subtracts 30 . His final answer is greater than 1000 . \( \begin{array}{ll}\text { (a) Using } x \text { to represent Niluka's integer, write down an inequality in } x \text {. }\end{array} \)

To represent Niluka's thoughts mathematically, we start with the integer \( x \). Here’s how it unfolds: First, he multiplies \( x \) by 6: \[ 6x \] Then, he subtracts 20: \[ 6x - 20 \] Next, he multiplies the result by 2: \[ 2(6x - 20) = 12x - 40 \] Finally, he subtracts 30: \[ 12x - 40 - 30 = 12x - 70 \] Now, as stated, his final answer is greater than 1000: \[ 12x - 70 > 1000 \] Therefore, the inequality we have is: \[ 12x - 70 > 1000 \] To complete this, we can add 70 to both sides: \[ 12x > 1070 \] Lastly, by dividing each side by 12, we find: \[ x > \frac{1070}{12} \] So, \( x > 89.1667 \). Given \( x \) is an integer, \( x \geq 90 \).