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How do I solve inequality and graph them

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5 Answers

4+2(-8p-1) ≥ -94

2(-8p-1) ≥ -98         subtract 4 from both sides

-8p-1 ≥ -49             divide both sides by 2

-8p ≥ -48                add 1 to both sides

p ≤ 6                     divide both sides by -8 and flip the direction of the sign (flip the direction of sign when multiplying/dividing by negative number)

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.

Destiny, I'll assume that the "_>" in your question means "greater than or equal to" (it's usually written >= on a computer).

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

-16p - 2 >= -98;

-16p >= -96;

p <= 6. (Remember, if you're dividing by a negative in an inequality, switch the direction of the sign!)

Solving an inequality is largely the same as solving an equation. The graphing is also quite similar.

The one, important rule change is that if you divide or multiply by a negative number you should flip the inequality sign to the other direction. For example:

-14x > 56  Divide both sides by -14 to isolate x but flip the inequality.

x  < -4

Graphing an inequality like this can be done with a number line. A small circle should be placed over the number. If the symbol has "or equal to" is it's description then you should darken the circle in. If it is just greater than, or lesser than ( >    or   <)  then you should use an open ring, don't fill in the circle. Finally draw a solid dark line down the number line in the direction of the inequality symbol.  It is tough to make a good presentation of it here but if you pretend that the capital O is an OPEN circle, then  x < -4 should be graphed as:

<________________________O

<-------------------------------------------------------------------------------------->

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

 

When graphing an inequality with two valuables you must use an XY grid, dotted or solid lines, and a shaded region, to represent the region of truth.  

 

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

2(-8p-1) > -98

-16p-2 > -98

-16p > -96

p > -96/-16

p > 6

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.