Solve 7 <= 3 - 2P < 11?

Question

I tutor in math, but I'm not sure how to do this type of inequality. When I went to school, inequalities were not stressed much.

Answer 1

Given:
7<=3-2p<11

You want to isolate p, and as long, we only add and subtract its OK as long we do it in every term in the inequality.

Of cause, we want to add -3 in the term in the middle, and therefore in rest of the expression, we get:
7-3<=3-3-2p<11-3 <=>
4<-2p<8
Now we want to divide with 2 and we can do so, as long, we do it in all term, but we also want to multiply with -1, but it's also OK if we remember to reverse the inequality sign.
This use to be the point of confusion in calculation with inequalities
However, it is easy to se that it is true
Ex 7<8 multiply with -1 gives
-7<-8 but that not true therefore we have to reverse the inequality sign, if we multiply with a negative number.

Back on track:

4<=-2p<8<=>
-4/2=> p >-8/2
.......NB!!.NB!!!
-2=>p>-4
Or if you better like the result in adequate form

x={ x in R l (-4 ================

Answer 2

7<=3-2P<11

there are two statements:
one 7<=3-2P and two, 3-2P<11

solutions:
* 7<=3-2P --- 7-3<=-2P --- 4/2<=-P then -2>=P
* 3-2P<11 --- -2P<11-3 --- -P<8/2 then P>-4

note that in this kind of equation when the minus on variables omitted, then the < or > is also opposited/conversed

Conclusion:
-2 >= P > -4 or P=-2,-3

Just put the number into the variable to try it out

Answer 3

7 <= 3 - 2P < 11

Subtract 3 from all sides, to get:

4 <= -2P < 7

Divide by negative 2 throughout, to get the following (and recall that when you mulitply or divide an inequality by a negative number, that you need to reverse the inequality sign):

2 >= P > -7

Did that help?

~ ♥ ~

Answer 4

7 ≤ 3 - 2P < 11

7 - 3 ≤ 3 - 2P - 3 < 11 - 3

4 ≤ - 2P < 8

4/-2 ≥ - 2P/-2 >8/- 2

- 2 ≥ P> - 4

The Inequality sign changes whenever dividion by a Negative number.

- - - - - - - -s-

Answer 5

3(2p-5)>8p-5 6p-15>8p-5 6p-8p>-5+15 -2p>10 2p<10 [be conscious opposite sense of inequality sign while multiplying by way of -a million p<5 p=15+6/11d that's already solved for p p-15=6/11d 11d(p-sixteen)=6 11d=6/(p-sixteen) d= 6/(p-sixteen) / 11 d= 6/(p-sixteen) / 11/a million d=6/(p-sixteen) X a million/11 d=6/[11(p-sixteen)] 7-4d< -3 -4d< -3-7 -4d< -10 4d>10 d>10/4 d>5/2

Answer 6

7-3<=-2p<11-3
-8<2p<=-4
-4
izzit the answer?

Answer 7

Aug, you need to have your morning coffee... ;-)

7<=3-2p<11

4<=-2p<8

-2>=p>-4