Question

How do you solve and graph `1/2x-4> -6`?

Answer 1

`x>4`, so shade all the graph above four, and use dotted line on the value 4 to say that value is not included

Explanation:

At the first take the `-4` to the other side so `-6` becomes `-2`
then multiply `-2` with `2` from the denominator of the other side so the inequality `x > 4` comes

Answer 2

`x > -4`

Explanation:

Given
`color(white)("XXX")1/2x-4 > -6`

Remember that we can
`color(white)("XXX")`add or subtract any number or
`color(white)("XXX")`multiply or divided any number greater than zero
on both sides of an inequality without changing the direction or validity of the inequality.

Adding `4` to both sides of the given inequality:
`color(white)("XXX")1/2x > -2`
Then multiplying both sides by `2`
`color(white)("XXX")x > -4`

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Note: I modified the question which contained the sequence ">-6" (and thus appeared as `>-6`) to "> -6" (so it appears as `> -6`). Hopefully this is what was intended.