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

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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