Question

Solving inequalities by multiplication and division
1. -8 < 8w

Answer 1

w > -1

Explanation:

Hello There!

We want to simplify this expression to be more specific we want to isolate the variable (w) using inverse operations

So we want to get rid of the 8 in 8w

8w is the same as 8 times w (multiplication)

The inverse of multiplication is division so to get rid of the 8 we want to divide by 8 but remember whatever we do to one side we want to do to the other side. So we divide each side by 8

-8/8 = - 1

8w/8=w

we're left with w > -1

Answer 2

`\huge\text{Hey there!}`

`\mathsf{-8 < 8w}`

`\large\text{TURN/FLIP the given EQUATION around}`

`\mathsf{8w > -8}`

`\large\text{DIVIDE 8 to BOTH SIDES}`

`\mathsf{(8w)/(8)>(-8)/(8)}`

`\large\text{Cancel out: }\mathsf{(8)/(8)}\large\text{ because that gives you 1}`

`\large\text{Keep: } \mathsf{(-8)/(8)}\large\text{ because that helps you compare to the w-value}`

`\large\text{New equation: } \mathsf{w>(-8)/(8)}`

`\mathsf{(-8)/(8)=\bf -1}`

`\mathsf{w>-1}`

`\mathsf{It\ is\ an\ O P E N\ circle\ shaded\ to\ the\RIGHT\, starting\ at\ the\ -1}`

`\boxed{\boxed{\large\text{Therefore, your \underline{answer} is: }\mathsf{\bf w > -1}}}\huge\checkmark`

`\text{Good luck on your assignment and enjoy your day!}`

~
`\frak{Amphitrite1040:)}`