Trouble with Inequalities problem

In summary: So "-5" is the correct answer. In summary, the problem is that x can be any real value, which means it can be negative as well. But when you multiply by a negative number, the inequality needs to be changed around. There are a few ways of solving this dilemma:- consider both cases, when x>0 and x<0 (x \neq 0)- solve both these cases normally like you would with any positive or negative number in place for the x. Then the solutions for both cases need to intersect (both must be satisfied).- Manipulate the fraction in such a way that you won't have the problem of multiplying through by a negative. Hint: a number
  • #1
crays
160
0
Hi, can someone tell me when should i change my sign when i have such a problem?

-(75/x) > 15

i find that if -75/x > 15
i could do :
-75 > 15x
-5 > x
x < -5.

or 75/-x > 15
i could do :
75 < -15x
-5 > x

which the answer in the book says -5 < x < 0

Thanks.
 
Physics news on Phys.org
  • #2


The problem is that x can be any real value, which means it can be negative as well. But when you multiply by a negative number, the inequality needs to be changed around. There are a few ways of solving this dilemma:

1) Consider both cases, when x>0 and x<0 ([tex]x \neq 0[/tex])

Solve both these cases normally like you would with any positive or negative number in place for the x. Then the solutions for both cases need to intersect (both must be satisfied).

2) Manipulate the fraction in such a way that you won't have the problem of multiplying through by a negative. Hint: a number squared is always positive.


p.s. graphmatica also makes the same mistake.
 
  • #3


crays said:
Hi, can someone tell me when should i change my sign when i have such a problem?

-(75/x) > 15

i find that if -75/x > 15
i could do :
-75 > 15x
-5 > x
x < -5.

or 75/-x > 15
i could do :
75 < -15x
-5 > x

which the answer in the book says -5 < x < 0

Thanks.
Neither -75> 15x nor 75< -15x is correct. You change the direction of the inequality when multiplying by a negative number, but it does NOT follow that "-x" is a negative number or that "x" is a positive number; that depends upon x.

If x is positive, then you can multiply on both sides by x to get -75> 15x so -5> x. But if x is positive, it can't be less than -5. If x is negative, then multiplying on both sides gives -75< 15x so -5< x. Since we have assumed that x is negative, that says -5< x< 0.
 

1. What are inequalities and why are they important in science?

Inequalities are mathematical expressions that compare two quantities and show their relationship using symbols such as greater than, less than, or not equal to. They are important in science because they allow us to describe and analyze relationships between variables and make predictions about outcomes.

2. How are inequalities used in scientific experiments?

Inequalities are used in scientific experiments to set limits or constraints on variables. For example, an experiment may have an inequality stating that a certain temperature must be maintained throughout the duration of the experiment. This helps ensure the validity and reliability of the results.

3. What is the difference between solving an inequality and solving an equation?

Solving an inequality involves finding a range of values that make the statement true, while solving an equation involves finding a specific value that makes the equation true. Inequalities also use different symbols, such as ≤ or ≥, while equations use the equal sign (=).

4. Can inequalities be graphed?

Yes, inequalities can be graphed on a number line or coordinate plane. The solution to the inequality is represented by a shaded region on the graph, with the boundary line representing the values that make the inequality true.

5. How can inequalities be applied in real-life situations?

Inequalities can be applied in a variety of real-life situations, such as budgeting, determining eligibility for programs, and analyzing data in fields such as economics, sociology, and environmental science. They can also be used to model and solve real-world problems, such as finding the optimal production level for a company.

Similar threads

Replies
8
Views
458
  • Precalculus Mathematics Homework Help
Replies
7
Views
557
  • Precalculus Mathematics Homework Help
Replies
29
Views
2K
  • Precalculus Mathematics Homework Help
Replies
10
Views
788
  • Precalculus Mathematics Homework Help
Replies
11
Views
1K
  • Precalculus Mathematics Homework Help
Replies
13
Views
2K
  • Precalculus Mathematics Homework Help
Replies
11
Views
967
  • Precalculus Mathematics Homework Help
Replies
7
Views
698
  • Precalculus Mathematics Homework Help
Replies
2
Views
442
Back
Top