Question

1. write an inequality for the product of 3.6 and an unknown number that is greater than 18. 5. simplify ( a^{3}x - |x^{3}| ) for ( a = -3 ) and ( x = -2 ).

Explanation:

Sub - Question 1: Write an inequality for the product of 3.6 and an unknown number that is greater than 18.

Step 1: Define the unknown number

Let the unknown number be \(x\).

Step 2: Find the product

The product of 3.6 and the unknown number \(x\) is \(3.6x\).

Step 3: Write the inequality

Since this product is greater than 18, the inequality is \(3.6x>18\).

Step 1: Substitute the values of \(a\) and \(x\) into the expression

First, substitute \(a=-3\) and \(x = - 2\) into \(a^{3}x-\vert x^{2}\vert\).
For \(a^{3}\), when \(a=-3\), \(a^{3}=(-3)^{3}=-27\) (because \((-3)\times(-3)\times(-3)=-27\)).
For \(x=-2\), \(x^{2}=(-2)^{2} = 4\), so \(\vert x^{2}\vert=\vert4\vert = 4\).

Step 2: Calculate the first term \(a^{3}x\)

Substitute \(a^{3}=-27\) and \(x = - 2\) into \(a^{3}x\), we get \((-27)\times(-2)=54\) (because the product of two negative numbers is positive).

Step 3: Calculate the second term \(\vert x^{2}\vert\)

We already found that \(\vert x^{2}\vert = 4\).

Step 4: Subtract the second term from the first term

Now, calculate \(a^{3}x-\vert x^{2}\vert\), which is \(54 - 4=50\).

Answer:

\(3.6x > 18\)

Sub - Question 2: Simplify \(a^{3}x-\vert x^{2}\vert\) for \(a = - 3\) and \(x=-2\).