SOLUTION: What values of x satisfy |x - 4| + 2(x + 3) <= 11 + 5|x + 7| + 3x + 8. Express your answer in interval notation.

Question 1209364: What values of x satisfy |x - 4| + 2(x + 3) <= 11 + 5|x + 7| + 3x + 8.
Express your answer in interval notation.
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

Simplify the inequality....

The behavior of the function changes when the arguments of the absolute value expressions are equal to 0 -- at x=4 and x=-7. That divides the number line into three intervals: (-infinity,-7], [-7,4], and [4,infinity)

Find the value on each interval that satisfy the inequality.

(1) (-infinity,-7]

On this interval, and

Of the values of x on the given interval (-infinity,-7], the ones that satisfy the inequality are those less than or equal to -26/3.

First part of solution set: (-infinity,-26/3]

(2) [-7,4]

On this interval, and

Of the value of x on the given interval [-7,4], the ones that satisfy the inequality are those greater than or equal to -44/7.

Second part of solution set: [-44/7,4]

(3) [4,infinity)

On this interval, and

All of the values of x on the given interval [4,infinity) are greater than or equal to -52/5.

Third part of solution set: [4,infinity)

ANSWER: the complete solution set is (-infinity,-26/3] U [-44/7,infinity)

The simplified form of the inequality I used is , which is equivalent to .

Here is a graph of that function showing the value is less than or equal to 0 on (-infinity,-26/3] U [-44/7,infinity).

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