Friday

July 25, 2014

July 25, 2014

Posted by **samantha** on Friday, September 23, 2011 at 9:06pm.

If 15 - 2x < 7, then for all possible values of x that make the inequality true,

(a) x<8

(b) x>8

(c) x>4

(d) x<4

(e) x>1/4

Answer:

i chose the answer (d) but the answer of the book said (c).

i understand where they are coming from we have to change the inequality sign due to the division we do. but i don't understand the logic. can someone kindly, please, explain the logic?

-Great Thank in advance =)

- math-logic(shsat) -
**MathMate**, Friday, September 23, 2011 at 9:09pm15 - 2x < 7

Add 2x to each side

15-2x+2x < 7+2x

or

15 < 7+2x

Switch sides (switch inequality sign also)

7+2x > 15

subtract 7

7-7+2x > 15-7

2x > 8

x > 4

So it's (c)

What's important is when you multiply inequalities by -1 (probably what you did), you have to reverse the direction of the inequality.

- math-logic(shsat) -
**samantha**, Friday, September 23, 2011 at 9:14pmoh okay so instead of starting with the integer(15) you're saying i should start with the number and variable(2x). then flip the equation?

im still confused i learned that you should start with the integer and leave the variable for the end.

i also didn't get the part when you said i multiplied my inequality with -1 because i didn't

BTW: thanks a lot for your explanation.

- math-logic(shsat) -
**MathMate**, Saturday, September 24, 2011 at 7:58pmBasically, you can start with either one, as long as you finish with all variables on one side, and numbers (or integers) on the other side of the inequality.

HOWEVER, if you multiply each side by a negative number (or -1), you must flip the direction of the inequality.

For example,

5x<20, then x<4 (divide each side by 5)

BUT

-3x > -18

Divide by NEGATIVE 3 to get

x**<**(-18)/(-3)

x**<**6

**Related Questions**

math - if 15-2x<7, then for all possible values of x that make the inequality...

math - can some one solve this Ex 1: -2x+7>22 -2x+7-7>22-7 -2x>15 -2x...

Phil103 Informal Logic - 1. Question : "~ P v Q" is best read as Student Answer...

math - |n+1|<4 How many values of the integer n will make the inequality a ...

math - Use an inequality to solve the problem. Be sure to show the inequality ...

discrete mathematics - problem has to do with three valued logic, ie the values ...

algebra - Jeremy is building a deck for the community center. The deck is shaped...

PHI103: Informal Logic - 1) In the truth table for an invalid argument, Student ...

logic - Truth tables can (Points : 1) display all the possible truth values ...

Informal Logic-Pls chk ans - The sentence "P → Q" is read as (3) P or Q P ...