Question

How do you graph `2(x-1)<=10`?

Answer 1

`2(x-1) ≤ 10`

`2(x-1)-10≤0`

`2x-2-10≤0`

`2x-12≤0`

Monotony properties will then be,

Explanation:

We can add everything together on one side of the equation.

`2(x-1)-10≤0`

From there we can multiply things out,

`2x-2-10≤0 => 2x-12≤0`

After that we can look at the monotony properties of the equation.
We will for example see that it has a zero point at `x=6`. So by that, we can test for which side of the zero point the equation is either positive or negative.

Trying to check with number `x=3`:
`2*(3)-12=-6`

So to the left on the `x=6`, we will have negative numbers. That means that on the right side, we must have positive numbers. But, we can check certaintly check that too.

Trying to check with number `x=9`:
`2*(9)-12=6`

So from there, we know that we will have positive to the right side.

When we graph something like this, we can see it as a linear line. And draw it like the image I have attached.