Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Let's solve the given absolute value inequality step by step:
Given:
[tex]\[ \frac{|x+15|}{5} \leq 26 \][/tex]
### Step 1: Clear the fraction
Multiply both sides of the inequality by 5 to eliminate the fraction:
[tex]\[ |x + 15| \leq 130 \][/tex]
### Step 2: Break down the absolute value inequality
The inequality [tex]\( |x + 15| \leq 130 \)[/tex] means that the expression inside the absolute value, [tex]\(x + 15\)[/tex], lies between [tex]\(-130\)[/tex] and [tex]\(130\)[/tex]. This can be written as two separate inequalities:
[tex]\[ -130 \leq x + 15 \leq 130 \][/tex]
### Step 3: Solve each inequality separately
First, solve the inequality on the left:
[tex]\[ -130 \leq x + 15 \][/tex]
Subtract 15 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ -130 - 15 \leq x \][/tex]
[tex]\[ -145 \leq x \][/tex]
Second, solve the inequality on the right:
[tex]\[ x + 15 \leq 130 \][/tex]
Subtract 15 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x \leq 130 - 15 \][/tex]
[tex]\[ x \leq 115 \][/tex]
### Conclusion
Combining the two inequalities, we have:
[tex]\[ -145 \leq x \leq 115 \][/tex]
### Positive Absolute Value
We need the positive absolute value for [tex]\(x\)[/tex]. Hence, we look at the upper bound of this range:
[tex]\[ x \leq 115 \][/tex]
Thus, the positive absolute value for [tex]\(x\)[/tex] is:
[tex]\[ 115 \][/tex]
Given:
[tex]\[ \frac{|x+15|}{5} \leq 26 \][/tex]
### Step 1: Clear the fraction
Multiply both sides of the inequality by 5 to eliminate the fraction:
[tex]\[ |x + 15| \leq 130 \][/tex]
### Step 2: Break down the absolute value inequality
The inequality [tex]\( |x + 15| \leq 130 \)[/tex] means that the expression inside the absolute value, [tex]\(x + 15\)[/tex], lies between [tex]\(-130\)[/tex] and [tex]\(130\)[/tex]. This can be written as two separate inequalities:
[tex]\[ -130 \leq x + 15 \leq 130 \][/tex]
### Step 3: Solve each inequality separately
First, solve the inequality on the left:
[tex]\[ -130 \leq x + 15 \][/tex]
Subtract 15 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ -130 - 15 \leq x \][/tex]
[tex]\[ -145 \leq x \][/tex]
Second, solve the inequality on the right:
[tex]\[ x + 15 \leq 130 \][/tex]
Subtract 15 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x \leq 130 - 15 \][/tex]
[tex]\[ x \leq 115 \][/tex]
### Conclusion
Combining the two inequalities, we have:
[tex]\[ -145 \leq x \leq 115 \][/tex]
### Positive Absolute Value
We need the positive absolute value for [tex]\(x\)[/tex]. Hence, we look at the upper bound of this range:
[tex]\[ x \leq 115 \][/tex]
Thus, the positive absolute value for [tex]\(x\)[/tex] is:
[tex]\[ 115 \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.