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

May 2, 2018

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 $x = 3$:
$2 \cdot \left(3\right) - 12 = - 6$

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 $x = 9$:
$2 \cdot \left(9\right) - 12 = 6$

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.