Question

Solve for x. 6x-10≤8 or 1/3 x+6>12

Answer 1

Answer: (-∞,3)∪(18,∞)

Explanation:

To solve this problem you must apply the proccedure shown below:

1. You must solve for x, as following:

`6x-10\leq8\\6x\leq18\\x\leq3`

`(1)/(3)x+6>12\\x>3(6)\\x>18`

2. Therefore, you have that the result is:

(-∞,3]∪(18,∞)

Answer 2

The solution is

`x\le 3 \:or \:x>18`

`<b><u>EXPLANATION</u></b>`

`6x-10\le 8\: or (1)/(3)x+6>12`

We group like terms, to obtain;

`6x\le 8+10\: or (1)/(3)x>12-6`

Simplify to get,

`6x\le 18\: or (1)/(3)x>6`

We further simplify to get;

`x\le 3\: or x>18`

This can also be rewritten as;

`x\le 3, x>18`

Or

`(-\infty 3] \cup (18,+ \infty)`

This can be represented on the number line as shown in the diagram.