Solve absolute value inequality. -3|x+7|\geq -27

Salvatore Boone 2021-12-17 Answered
Solve absolute value inequality.
3|x+7|27
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Expert Answer

Bubich13
Answered 2021-12-18 Author has 36 answers

Step 1
An absolute value inequality is an equation of the form AB, or A∣≥B, where an expression A (and possibly but not usually B) depends on a variable x. Solving the inequality means finding the set of all x that satisfy the inequality. Usually this set will be an interval or the union of two intervals.
Step 2
We have,
3|x+7|27
On using the property of inequality axbx(b)(a), we get the result as
3|x+7|27
|x+7|273
|x+7|9...(1)
Now, we know that for an inequality
|x|a
axa
Using the above concept in equation (1), we get the result as
|x+7|9
9x+79
97x97
16x2
Hence, values of x lies between [-16,2].

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vicki331g8
Answered 2021-12-19 Author has 37 answers
Step 1
To Determine:
Solve absolute value inequality.
Given: we have 3|x+7|27
Explanation: we have
3|x+7|27
multiply both the sides with negative sign then the sign of inequality get reverse
3|x+7|27
now divide the inequality by 3 in both sides then we have
3|x+7|3273
|x+7|9
Step 2
now we can write the above inequality as
1) x+79
x2
2) x+79
x16
so we have
Answer: x2 and x16

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