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

1 Answer
May 2, 2018

Answer:

#2(x-1) ≤ 10#

# 2(x-1)-10≤0#

#2x-2-10≤0#

#2x-12≤0#

Monotony properties will then be,

enter image source here

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.