Question

Question 1

The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.

a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weights. Use x
as the variable.

Answer 1

Answer:To find the minimum and maximum acceptable soccer ball weights, we can set up an absolute value equation using the variable x.

The recommended weight of the soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.

Let's set up the equation:

| x - 430 | ≤ 20

The absolute value of x minus 430 should be less than or equal to 20.

To solve this equation, we can break it down into two separate equations:

1. x - 430 ≤ 20

In this case, we add 430 to both sides of the equation:

x ≤ 450

2. -(x - 430) ≤ 20

We multiply -1 to both sides of the equation to remove the negative sign:

x - 430 ≥ -20

Then, we add 430 to both sides of the equation:

x ≥ 410

So, the minimum acceptable soccer ball weight is 410 grams (x ≥ 410) and the maximum acceptable soccer ball weight is 450 grams (x ≤ 450).

This means that any soccer ball weight within the range of 410 grams to 450 grams is considered acceptable.

Answer 2

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

b) Solution: 410 ≤ x ≤ 450

Step-by-step 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 accepted variation (difference) is up to 20 g means that the difference has to be 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