Question

How do you solve `-x/5+12<4` and graph on the number line?

Answer 1

`x>40`

Notice that the 'blob' at the left hand side of the red line on the axis is `color(red)(ul("not filled in"))`. This means that `x` does not actually take on the value of 40.

Explanation:

Multiply both sides by (-1) to make the x term positive. Note that this act turns the inequality sign the other way round.

`-x/5+12 < 4" "->" "+x/5-12 > -4`
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`color(blue)("Why does it turn the inequality round?")`

Consider `a>3`

In this instance `a` is positive and greater than 3. So for example
`4 > 3`

What happens if we multiply by (-1) but not change the sign round? We get this: `-4 > -3` Clearly this is wrong so we need to reverse the sign. Thus `(-1)(a>3)" becomes "-a< -3`
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`color(blue)("Continuing the answer")`

Add 12 to both sides giving:

`x/5 > 8`

Multiply each side by 5

`" "color(green)(ul(bar( |color(white)(./.)x>40color(white)(./.)|)))`
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