At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve the absolute value inequality [tex]\( |x + 2| \leq 3 \)[/tex], we start by understanding that the absolute value inequality [tex]\( |A| \leq B \)[/tex] can be rewritten as two simultaneous inequalities: [tex]\(-B \leq A \leq B\)[/tex].
For the given inequality [tex]\( |x + 2| \leq 3 \)[/tex]:
1. We split the absolute value inequality into two inequalities:
[tex]\[ -3 \leq x + 2 \leq 3 \][/tex]
2. We now solve each part of this compound inequality separately.
3. First, solve the left side of the compound inequality:
[tex]\[ -3 \leq x + 2 \][/tex]
Subtract 2 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ -3 - 2 \leq x \][/tex]
[tex]\[ -5 \leq x \][/tex]
4. Next, solve the right side of the compound inequality:
[tex]\[ x + 2 \leq 3 \][/tex]
Subtract 2 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x \leq 3 - 2 \][/tex]
[tex]\[ x \leq 1 \][/tex]
5. Combine both inequalities to get the final solution:
[tex]\[ -5 \leq x \leq 1 \][/tex]
Thus, the solution to the absolute value inequality [tex]\( |x + 2| \leq 3 \)[/tex] is:
[tex]\[ -5 \leq x \leq 1 \][/tex]
From the given options, the correct interval is:
[tex]\[ -5 \leq x \leq 1 \][/tex]
Therefore, the correct answer is:
[tex]\[ -5 \leq x \leq 1 \][/tex]
For the given inequality [tex]\( |x + 2| \leq 3 \)[/tex]:
1. We split the absolute value inequality into two inequalities:
[tex]\[ -3 \leq x + 2 \leq 3 \][/tex]
2. We now solve each part of this compound inequality separately.
3. First, solve the left side of the compound inequality:
[tex]\[ -3 \leq x + 2 \][/tex]
Subtract 2 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ -3 - 2 \leq x \][/tex]
[tex]\[ -5 \leq x \][/tex]
4. Next, solve the right side of the compound inequality:
[tex]\[ x + 2 \leq 3 \][/tex]
Subtract 2 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x \leq 3 - 2 \][/tex]
[tex]\[ x \leq 1 \][/tex]
5. Combine both inequalities to get the final solution:
[tex]\[ -5 \leq x \leq 1 \][/tex]
Thus, the solution to the absolute value inequality [tex]\( |x + 2| \leq 3 \)[/tex] is:
[tex]\[ -5 \leq x \leq 1 \][/tex]
From the given options, the correct interval is:
[tex]\[ -5 \leq x \leq 1 \][/tex]
Therefore, the correct answer is:
[tex]\[ -5 \leq x \leq 1 \][/tex]
Which of the following is a direct result of the Spanish-American War?
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.