Question

How do you solve and graph `2(-3m - 5) ≥ -28`?

Answer 1

`m<=3`

Explanation:

Manipulate the inequality as you would an equation. However there is a trap when doing so. If you multiply by negative one then you turn the inequality round the other way. I will show you why in the explanation.

Given:`" "2(-3m-5)>=-28" ".............Equation(1)`

Divide both sides by 2 (gets rid of the 2 on the left)

`-3m-5>= -14`

Add 5 to both sides (gets rid of the 5 on the left)

`-3m>= -9`

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Method 1:

`-3m>= -9`

Multiply both sides by (-1)

`color(magenta)(+3m<=+9)" ".....Equation(2)`
......................................................................
Method 2:

`-3m>= -9`

Add `3m` to both sides

`0 >=3m-9`

Add 9 to both sides

`+9>=+3m`

Write as:

`color(magenta)(3m<=+9)" "............Equation(3)`
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Notice that both `Equation(2) and Equation(3)` are the same
This demonstrates why you turn the inequality round the other way when you multiply by negative one

`3m<=9`

Divide both sides by 3

`m<=3`