Question

use the graph of f(x) = x to find the maximum such that x − 4 < 0.4 whenever |x − 16| < . (round your answer to two decimal places.)

Answer 1

The maximum value of
`\(x\)` such that
`\(x - 4 < 0.4\)` whenever
`\(|x - 16| < 4\) is \(16.4\).`

Step-by-step explanation:

The given inequality
`\(x - 4 < 0.4\)`implies that
`\(x < 4.4\)`.

The second inequality
`\(|x - 16| < 4\)` can be broken down into two separate inequalities:
`\(x - 16 < 4\) and \(-(x - 16) < 4\)`,

which simplify to
`\(x < 20\) and \(x > 12\)`, respectively.

Combining these conditions, we find that
`\(x\)` must be less than
`\(4.4\)` and satisfy
`\(12 < x < 20\)`. Therefore, the maximum value of
`\(x\)` that satisfies these conditions is
`\(16.4\)`.