 # Solve absolute value inequality. -3|x+7|\geq -27 Salvatore Boone 2021-12-17 Answered
Solve absolute value inequality.
$-3|x+7|\ge -27$
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Step 1
An absolute value inequality is an equation of the form $\mid A\mid B$, or $\mid A\mid \ge B$, 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,
$-3|x+7|\ge -27$
On using the property of inequality $-ax\ge -b⇒x\le \frac{\left(-b\right)}{\left(-a\right)}$, we get the result as
$-3|x+7|\ge -27$
$|x+7|\le \frac{-27}{-3}$
$|x+7|\le 9$...(1)
Now, we know that for an inequality
$|x|\le a$
$-a\le x\le a$
Using the above concept in equation (1), we get the result as
$|x+7|\le 9$
$-9\le x+7\le 9$
$-9-7\le x\le 9-7$
$-16\le x\le 2$
Hence, values of x lies between [-16,2].

We have step-by-step solutions for your answer! vicki331g8
Step 1
To Determine:
Solve absolute value inequality.
Given: we have $-3|x+7|\ge -27$
Explanation: we have
$-3|x+7|\ge -27$
multiply both the sides with negative sign then the sign of inequality get reverse
$3|x+7|\le 27$
now divide the inequality by 3 in both sides then we have
$\frac{3|x+7|}{3}\le \frac{27}{3}$
$|x+7|\le 9$
Step 2
now we can write the above inequality as
1) $x+7\le 9$
$x\le 2$
2) $x+7\ge -9$
$x\ge -16$
so we have

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