Question

The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write and solve an absolute value inequality for the range of acceptable widths.

Answer 1

`4.65\leq x\leq 5.35`

Explanation:

Let the actual width of belt be x

we are given that the ideal width of safety belt strap is 5 cm

So, Difference between actual and ideal = (x-5)cm

We are also given that An actual width can vary by at most 0.35 cm.

So, The difference between actual and ideal width should be less than or equal to 0.35 cm

So,
`|x-5|\leq 0.35`

We know

`x-5\leq 0.35` and
`x-5\geq -0.35`

`x\leq 0.35+5` and
`x\geq -0.35+5`

`x\leq 5.35` and
`x\geq 4.65`

So,
`4.65\leq x\leq 5.35`

Hence the range of acceptable widths is
`4.65\leq x\leq 5.35`