QuestionExpress the RDI of a supplement ( $800 \mathrm{mg}$ ) with a variation of $\pm 80 \mathrm{mg}$ using an absolute value inequality. Solve it.

Studdy Solution

STEP 1

Assumptions1. The recommended daily intake (RDI) of the supplement is800mg/day. The actual supplement needs can vary by plus or minus80mg

STEP 2

We need to write an absolute value inequality to express the RDI plus or minus80mg. The absolute value of a difference is used when we want to capture a range of values that deviate from a certain value by a certain amount. In this case, we want to capture the values that deviate from the RDI (800mg) by80mg.
$|x - RDI| \leq Variation$

STEP 3

Now, plug in the given values for the RDI and the variation to write the absolute value inequality.
$|x -800| \leq80$ So, the correct answer is C. $|x-800| \leq80$

STEP 4

To solve the inequality, we need to consider two cases. One where the quantity inside the absolute value is positive and one where it is negative.
Case1 $x -800 \leq80$
Case2 $-(x -800) \leq80$

STEP 5

olve the inequality for case1.
$x -800 \leq80$
$x \leq800 +80$
$x \leq880$

STEP 6

olve the inequality for case2.
$-(x -800) \leq80$
$x -800 \geq -80$
$x \geq800 -80$
$x \geq720$

STEP 7

Combine the results of the two cases to find the range of values for x.
$720 \leq x \leq880$
So, the daily intake of the supplement should be between720mg and880mg.

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QuestionExpress the RDI of a supplement ( $800 \mathrm{mg}$ ) with a variation of $\pm 80 \mathrm{mg}$ using an absolute value inequality. Solve it.

Studdy Solution

STEP 1

Assumptions1. The recommended daily intake (RDI) of the supplement is800mg/day. The actual supplement needs can vary by plus or minus80mg

STEP 2

STEP 3

Now, plug in the given values for the RDI and the variation to write the absolute value inequality.
$|x -800| \leq80$ So, the correct answer is C. $|x-800| \leq80$

STEP 4

To solve the inequality, we need to consider two cases. One where the quantity inside the absolute value is positive and one where it is negative.
Case1 $x -800 \leq80$
Case2 $-(x -800) \leq80$

STEP 5

olve the inequality for case1.
$x -800 \leq80$
$x \leq800 +80$
$x \leq880$

STEP 6

olve the inequality for case2.
$-(x -800) \leq80$
$x -800 \geq -80$
$x \geq800 -80$
$x \geq720$

STEP 7

Combine the results of the two cases to find the range of values for x.
$720 \leq x \leq880$
So, the daily intake of the supplement should be between720mg and880mg.

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QuestionExpress the RDI of a supplement (800mg800 \mathrm{mg}800mg) with a variation of ±80mg\pm 80 \mathrm{mg}±80mg using an absolute value inequality. Solve it.

Studdy Solution

STEP 1

Assumptions1. The recommended daily intake (RDI) of the supplement is800mg/day. The actual supplement needs can vary by plus or minus80mg

STEP 2

STEP 3

Now, plug in the given values for the RDI and the variation to write the absolute value inequality.∣x−800∣≤80|x -800| \leq80∣x−800∣≤80So, the correct answer is C. ∣x−800∣≤80|x-800| \leq80∣x−800∣≤80

STEP 4

To solve the inequality, we need to consider two cases. One where the quantity inside the absolute value is positive and one where it is negative.Case1 x−800≤80x -800 \leq80x−800≤80Case2 −(x−800)≤80-(x -800) \leq80−(x−800)≤80

STEP 5

olve the inequality for case1.x−800≤80x -800 \leq80x−800≤80x≤800+80x \leq800 +80x≤800+80x≤880x \leq880x≤880

STEP 6

olve the inequality for case2.−(x−800)≤80-(x -800) \leq80−(x−800)≤80x−800≥−80x -800 \geq -80x−800≥−80x≥800−80x \geq800 -80x≥800−80x≥720x \geq720x≥720

STEP 7

Combine the results of the two cases to find the range of values for x.720≤x≤880720 \leq x \leq880720≤x≤880So, the daily intake of the supplement should be between720mg and880mg.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionExpress the RDI of a supplement ( $800 \mathrm{mg}$ ) with a variation of $\pm 80 \mathrm{mg}$ using an absolute value inequality. Solve it.

Now, plug in the given values for the RDI and the variation to write the absolute value inequality.
$|x -800| \leq80$ So, the correct answer is C. $|x-800| \leq80$

To solve the inequality, we need to consider two cases. One where the quantity inside the absolute value is positive and one where it is negative.
Case1 $x -800 \leq80$
Case2 $-(x -800) \leq80$

olve the inequality for case1.
$x -800 \leq80$
$x \leq800 +80$
$x \leq880$

olve the inequality for case2.
$-(x -800) \leq80$
$x -800 \geq -80$
$x \geq800 -80$
$x \geq720$

Combine the results of the two cases to find the range of values for x.
$720 \leq x \leq880$
So, the daily intake of the supplement should be between720mg and880mg.