Solve absolute value inequality. −3|x+7|≥−27

Question

Solve absolute value inequality.  −3|x+7|≥−27

Bubich13 · Accepted Answer

Step 1
An absolute value inequality is an equation of the form $∣ A ∣ B$ , or $∣ A ∣\geq B$ , 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,
$- 3 | x + 7 | \geq - 27$
On using the property of inequality $- a x \geq - b \Rightarrow x \leq \frac{(- b)}{(- a)}$ , we get the result as
$- 3 | x + 7 | \geq - 27$
$| x + 7 | \leq \frac{- 27}{- 3}$
$| x + 7 | \leq 9$ ...(1)
Now, we know that for an inequality
$| x | \leq a$
$- a \leq x \leq a$
Using the above concept in equation (1), we get the result as
$| x + 7 | \leq 9$
$- 9 \leq x + 7 \leq 9$
$- 9 - 7 \leq x \leq 9 - 7$
$- 16 \leq x \leq 2$
Hence, values of x lies between [-16,2].

vicki331g8 · Accepted Answer

Step 1
To Determine:
Solve absolute value inequality.
Given: we have

- 3 | x + 7 | \geq - 27

Explanation: we have

- 3 | x + 7 | \geq - 27

multiply both the sides with negative sign then the sign of inequality get reverse

3 | x + 7 | \leq 27

now divide the inequality by 3 in both sides then we have

\frac{3 | x + 7 |}{3} \leq \frac{27}{3}

| x + 7 | \leq 9

Step 2
now we can write the above inequality as
1)

x + 7 \leq 9

x \leq 2

2)

x + 7 \geq - 9

x \geq - 16

so we have
Answer:

x \leq 2 and x \geq - 16

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

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