Question

he ideal width of a safety belt strap for a certain automobile is 6 cm. An actual width can vary by at most 0.4 cm. Write an absolute value inequality for the range of acceptable widths. Picture of possible answers included.

Answer 1

1. The width of the safety belt is 6 cm, but it can vary by at most 0.4 cm

this means that the width can be at most: 6+0.4= 6.4 (cm)

and at least 6-0.4=5.6 (cm)

so the width x, is represented by the inequality

 $5.6 \leq x \leq 6.4$

$6-0.4 \leq x \leq 6+0.4$

subtract 6 from all sides:

$-0.4 \leq x-6 \leq 0.4$

from the rule : $|A(x)| \leq c$ is equivalent to 

$-c \leq A(x) \leq c$ we have:

$|x-6| \leq 0.4$ 

Answer 2

Answer: $0.4\geq | x-6|$

Step-by-step explanation:

Here the  ideal width of a safety belt strap for a certain automobile = 6 cm

And, according to the question,

It can be only vary by at most 0.4 cm.

Thus, the maximum possible width = 6 + 0.4 = 6.4  cm

And the minimum possible width = 6 - 0.4 = 5.6 cm

Let x represents the width of the belt strap after a certain variation,

Then we can write,

$5.6\leq x\leq 6.4$

By subtracting 6 from all sides of the inequality,

$5.6 - 6\leq x\leq 6.4 - 6$

⇒ $- 0.4\leq x-6\leq 0.4$

If $- 0.4\leq x-6$

⇒$0.4\geq -(x-6)$

But, $0.4\geq x-6$

On combining the inequalities,

we get,  $0.4\geq |x-6|$