how do u solve |d-620| ≤ 0.05d?

Question

www.Jmap.org

how do u find the minimum and maximum values for d?

Answer 1

OK!

Those vertical lines denote "absolute value", so the sign of the result of whatever expression is inside is converted to positive.

Thus, you need to solve two problems for the answer:

-(d-620) ≤ 0.05d
and
d-620≤0.05d

-(d-620) ≤ 0.05d
620-d≤0.05d
620≤1.05d
590.4≤d

and

d-620≤0.05d
0.95d≤620
d≤652.6

Putting it together:
590.4≤d≤652.6

Done.

Answer 2

Whenever you have a positive number and absolute values in variables dealing with inequalities, you will either have:

1) |y| < a {or |y| <= a}
2) |y| > a {or |y| >= a}

In case #1, you will have a conjunction of inequalities (i.e. an AND), and

|y| < a translates to
(y < a) AND (y > -a) {or, in a simple step, -a < y < a}

In case #2, you will have a disjunction of inequalities (i.e an OR), and

|y| > a translates to
(y > a) OR (y < -a)

In your case, since you have "less than or equal to", you will be dealing with an AND.

|d - 620| <= 0.05d

{if d is a negative number, there is no solution, so let's assume d is a positive number.}

Thus, this becomes

[d - 620 <= 0.05d] AND [d - 620 >= -0.05d]

Dealing with these inequalities one at a time,

d - 620 <= 0.05d
d - 0.05d <= 620
0.95d <= 620
95d <= 62000
d <= 62000/95
d <= 12400/19

d - 620 >= -0.05d
1.05d >= 620
105d >= 62000
d >= 62000/105
d >= 12400/21

Therefore, 12400/21 <= d <= 12400/19

is your solution set.

Your minimum value is 12400/21 (which you can approximate with a calculator), and your maximum value is 12400/19.

Answer 3

You can do this too:

d-620 is non negative is d is greater or equals than 620

So, you can write the equation without the l l :

d-620 ≤ 0.05d

d- 0.05d ≤ 620

0.95 d ≤ 620

And, since 0.95 is positive, you can divide by it:

620≤ d ≤ 620/0.95

Let's now consider the second case, d is less than 620, so d-610 is negative.

So, you have to change its sign if you want to solve the equation without using l l:

-d +620 ≤ 0.05d

-0.05d - d ≤ -620

- 1.05 d ≤ -620

Now, since -1.05 is negative, you have to change the inequality sign

620/1.05≤ d <620

So, if you consider the union of the 2 solutions sets, d must be greater than 610/1.05 and less than 610/0.95

Just pick a calculator and that's it. And use as many digits as you want to, I disagree with the next answer, if you are working in Physics, then the amount of digits is important because of the error calculations. If you are working in Mathematics, then you should express 610/1.05 as an irreductible fraction

Answer 4

When you have an absolute value inequality equation, you must treat it as two equations.

d - 620 ≤ .05d and d - 620 ≥ -.05d

you remove the absolute value symbols on the first equation, and on the second, you switch the sign and make it negative.

-620 ≤ -.95d -620 ≥ -1.05d
d ≤ 652 12/19 d ≥590 10/21

(590 10/21) ≤ d ≤ (652 12/19)

hope this helps

Answer 5

|d-620| ≤ 0.05d
d-620 ≤ 0.05d
d - 0.05d ≤ 620
0,95d ≤ 620
d ≤ 620 : 0,95
d ≤ 652,63

and
|d-620| => -0.05d
d + 0.05d => 620
1.05d => 620
d => 620 : 1,05
d => 590,47
Solution: {d E R | 590.47 <= d <= 652.63}

Answer 6

in solving mod we solve eq in two ways :
|d-620|<=.05d
first by taking the value as positive
d-620<=.05d
-620<=-0.95d
620>=0.95d
620/0.95>=d

secondly by taking the value as negative
-d+620<=.05d
d-620>=-.05d
-620>=-1.05d
620<=1.05d
620/1.05<=d

620/1.05<=d<=620/0.95
590.4<=d<=652.6

Answer 7

All of the above answers are incorrect to a certain extent. One thing I learned in Math is to keep the answer in the same form as the question. Answer one is incorrect because .05d is in two decimal form and the first anser is in one decimal form and the second answer is incorrect because it is in fraction form. Since the .05d is in two decimal form so must be the answer...

{d:590.48<=d<=652.63}

Answer 8

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