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------- -1-------0------1-------2-------3-------4------5------6------7------8----->

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.

## Comments

You have not flipped the inequality sign when dividing by -16 at step 4, and therefore this answer is incorrect. Please check and fix.

4+2(-8p-1)> -94

2(-8p -1) > -98 Good subtract 4 from both sides.

-16p - 2 > -98 Good, clear parenthesis by distributing the 2 to -8p and -1.

-16p > -96 Good, Add 2 to both sides to clear -2 from the left side.

p > -96/-16 Wrong, yes divide both sides by -16, but remember to flip the inequality sign here, because you are dividing by a

negative number.

p < -96/-16 This is better and now the solution is:

P < 6

CHECK, pick a number less than 6, say 4.

4 + 2(-8(4)-1) > -94

4 + 2(-32-1) > -94

4 + 2(-33) > -94

4 + -66 > -94

-62 > -94, a true statement, so 4 works, as will any number < 6.

If you try a number > 6, say 8. it will lead to:

-126 > -94 and UNtrue statement.