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The recommended weight of a soccer ball is 430 G the actual weight is allowed to vary by up to 20 grams write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weight use x as the variable

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meerkat18
When you say recommended weight, it doesn't have to be required that the weight is 430 grams. It just means that it would be optimal if the weight was 430 grams. However, the weight could technically vary. It's given that it would vary by 20 grams. Thus, it could be 20 grams less than the recommended weight, or 20 grams more. The important thing is the recommended weight is the baseline.

To form an equation, we let x be the actual weight of the soccer ball. This weight is a range, from minimum to maximum requirements. 

x = 430 grams +/- 20 grams

The plus sign is for the maximum weight which is equal to 430 + 20 = 450 grams. On the other hand, the minimum weight is 430 grams - 20 grams = 410 grams. Therefore, the soccer ball's weight could vary between 410 grams to 450 grams. These are the limits.
Edufirst

Answer:

a) The absolute value equation is |x - 430| ≤ 20

b) Solution: 410 ≤ x ≤ 450

Explanation:

1) Call x the variable, actual weight of the soccer ball

2) Recomended weight: 430 g

3) Difference using absolute value is | x - 430|

4) The accepeted variation (difference) is up to 20 g means that the difference has to less than or equal to 20 g ⇒ | x - 430| ≤ 20

5) Solution:

i) start: |x - 430| ≤ 20

ii) as per the definition of absolute value: -20 ≤ x - 430 ≤ 20

iii) addition property of inequalities: add 430 to all the parts:

- 20 + 430 ≤ x - 430 + 430 ≤ 20 + 430

iv) do the operations: 410 ≤ x ≤ 450

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