```Question 554529

{{{8-4x>x-12}}} Distribute.

{{{-4x>x-12-8}}} Subtract {{{8}}} from both sides.

{{{-4x-x>-12-8}}} Subtract {{{x}}} from both sides.

{{{-5x>-12-8}}} Combine like terms on the left side.

{{{-5x>-20}}} Combine like terms on the right side.

{{{x<(-20)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number.

{{{x<4}}} Reduce.

----------------------------------------------------------------------

So the solution is {{{x<4}}}

The graph is

{{{drawing(500,80,-6, 14,-10, 10,
number_line( 500, -6, 14),

arrow(4,0,-6,0),
arrow(4,0.30,-6,0.30),
arrow(4,0.15,-6,0.15),
arrow(4,-0.15,-6,-0.15),
arrow(4,-0.30,-6,-0.30),

circle(4,0,0.3),
circle(4,0,0.3),
circle(4,0,0.3),
circle(4,0,0.3-0.02)
)}}}

Note: there is an open circle at the endpoint.

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Jim
```