Use the graph of
to solve the inequality
​

4+2(-8p-1)_>-94   solve for p

I will presume that _> means greater than or equal to

First we will subtract 4 from both sides yielding

2(-8p-1) _> -98                         Remember subtracting a positive from a negative makes it more negative

Distribute the 2 over the parenthetical "sum" keeping signs in mind

-16p-2 _> -98

Add 2 to both sides

-16p _> -96                             Remember adding a positive to a negative makes it less negative

NOW we need to observe the difference between solving inequalities and solving equalities:

Whenever an inequality is solved by multiplying or dividing both sides by a NEGATIVE, the sense of the inequality must be reversed!

Divide both sides by -16 to get 1p

p _< 6                        NOTE THE REVERSAL OF THE INEQUALITY SENSE

When p=6, the sides will be equal as would be expected

4+2(-8*6-1)=4+2(-48-1)=4+2(-49)=4-98=-94 which is _> -94

If p=7      (p>6)

4+2(-8*7-1)=4+2(-56-1)=4+2(-57)=4-114=-110 which is NOT >-94

If p=5      (p<6)

4+2(-8*5-1)=4+2(40-1)=4+2(--41)=4-82=-78 which IS _>-94

To plot p _< 6 use a number line <--- -2 -1012345678>

Put a solid dot on the 6, (because of the "or equal"), a line going negative from the 6 and an arrow on it.

I can't do the dot or second arrow due to typing limitations

If the inequality were not "or equals", the 6 would be surrounded by an open circle.

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Step-by-step explanation:

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step-by-step explanation: