Question

Which number line represents the solution set for the inequality 2x- 6>6 (x-2)+8

Answer 1

Answer:

The inequality is

2 x - 6 > 6(x -2) +8

To solve the inequality we will first use distributive property with respect to multiplication over subtraction

And then bring constant on one side and variable on another side keeping the inequality maintained

2 x -6 > 6 x -12 + 8

2 x -6 > 6 x - 4

6 x - 2 x< -6+4

4 x < -2

Dividing both sides by 2

x <  $\frac{-1}{2}$

Now i will draw the graph of above function.

Answer 2

we have that

$2x-6 > 6*(x-2)+8\\ 2x-6 > 6x-12+8\\ 2x-6x > -4+6\\ -4x > 2\\\\ x < -\frac{2}{4} \\\\ x$

using a graph tool

see the attached figure

the answer is

$x < -\frac{1}{2}$