Chapter 4.CM, Problem 46CM

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# For problems 43-56, solve the inequality and express the solution in interval notation. | 2 x + 6 | ≥ 20 .

To determine

To Find:

The inequality and express the solution in interval notation.

Explanation

Procedure used:

The values of |x| takes value depending on the sign of x.

When, x<0,

|x|=âˆ’x

When, xâ‰¥0,

|x|=x

The way of representing a set of numbers satisfying an inequality aâ‰¤xâ‰¤b in terms of interval is given by xâˆˆâ€‰[a,b].

An inequality xâ‰¥c is given by xâˆˆâ€‰[c,âˆž).

An inequality x<d is given by xâˆˆâ€‰(âˆ’âˆž,d).

Calculation:

The given inequality problem is |2x+6|â‰¥20.

Write the given inequalities as two inequalities.

(2x+6)â‰¥20â€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ‹…â‹…â‹…(1)

And,

âˆ’(2x+6)â‰¥20â€Šâ€Šâ€Šâ€Šâ€Šâ€Š&#

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