Question

How do you solve and graph `10-x>=3`?

Answer 1

`x<=7`

Explanation:

Using a shortcut tick

To make the `x` positive multiply both sides by (-1). However, in doing this the inequality sign must be turned round the other way.

`color(green)(10-x>=3" "->" "-10+x<=-3)`

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`color(brown)("Why does the sign turn round?")`

Using first principles

`10-x>=3`

Add `x` to both sides

`10+0>=3+x`

Subtract 3 from both sides

`10-3>=x`

this is the same as:

`x<=10-3`

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`color(brown)("Continuing the solution")`

Add 10 to both sides

`color(green)(-10+x<=-3" "->" "0+x<=10-3`

`color(green)(x<=10-3" "->" "x<=7)`