Question

Solve the following inequality,
`(4a)/(3)`≥ 2 ,representing each solution on a number line.

Answer 1

4a/3≥ 2

4a/3*3≥ 2*3

4a≥6

4a/4≥6/4

a≥3/2

On a number line, you would plot 3/2 with a filled in hole. The arrow you would draw to is the one that goes to the positive side, to the right. That's how to plot it.

Explanation:

Answer 2

To solve the inequality, we need to get the variable on one side and the constant on the other side. We can start by multiplying both sides of the inequality by 3:

`4a ≥ 6`

Now, we can divide both sides by 4:

`a ≥ (3)/(2)`

The solution to this inequality is all values of a that are greater than or equal to 3/2. We can represent this on a number line as:

(-infinity, -1.5) U [1.5, infinity)

Where ( -infinity, -1.5) represents all values less than -1.5 and [1.5, infinity) represents all values greater than or equal to 1.5.

Note that the solution can also be represented as a >= 1.5.