Get detailed and accurate responses to your questions on IDNLearn.com. Find the solutions you need quickly and accurately with help from our knowledgeable community.
Sagot :
To solve the compound inequality [tex]\(-7 \leq 6x + 5 \leq 23\)[/tex], we will follow these steps:
1. Isolate the term involving [tex]\(x\)[/tex]:
We start with the inequality:
[tex]\[ -7 \leq 6x + 5 \leq 23 \][/tex]
To isolate [tex]\(6x\)[/tex], we need to eliminate the constant term [tex]\(+5\)[/tex] that is added to [tex]\(6x\)[/tex]. We do this by subtracting 5 from all three parts of the inequality:
[tex]\[ -7 - 5 \leq 6x + 5 - 5 \leq 23 - 5 \][/tex]
Simplifying each part gives us:
[tex]\[ -12 \leq 6x \leq 18 \][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now that we have [tex]\(-12 \leq 6x \leq 18\)[/tex], we need to solve for [tex]\(x\)[/tex] by undoing the multiplication by 6. We do this by dividing all three parts of the inequality by 6:
[tex]\[ \frac{-12}{6} \leq \frac{6x}{6} \leq \frac{18}{6} \][/tex]
Simplifying each part gives us:
[tex]\[ -2 \leq x \leq 3 \][/tex]
So, the solution to the compound inequality [tex]\(-7 \leq 6x + 5 \leq 23\)[/tex] is:
[tex]\[ -2 \leq x \leq 3 \][/tex]
Therefore, the correct answer is:
d. [tex]\(-2 \leq x \leq 3\)[/tex]
1. Isolate the term involving [tex]\(x\)[/tex]:
We start with the inequality:
[tex]\[ -7 \leq 6x + 5 \leq 23 \][/tex]
To isolate [tex]\(6x\)[/tex], we need to eliminate the constant term [tex]\(+5\)[/tex] that is added to [tex]\(6x\)[/tex]. We do this by subtracting 5 from all three parts of the inequality:
[tex]\[ -7 - 5 \leq 6x + 5 - 5 \leq 23 - 5 \][/tex]
Simplifying each part gives us:
[tex]\[ -12 \leq 6x \leq 18 \][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now that we have [tex]\(-12 \leq 6x \leq 18\)[/tex], we need to solve for [tex]\(x\)[/tex] by undoing the multiplication by 6. We do this by dividing all three parts of the inequality by 6:
[tex]\[ \frac{-12}{6} \leq \frac{6x}{6} \leq \frac{18}{6} \][/tex]
Simplifying each part gives us:
[tex]\[ -2 \leq x \leq 3 \][/tex]
So, the solution to the compound inequality [tex]\(-7 \leq 6x + 5 \leq 23\)[/tex] is:
[tex]\[ -2 \leq x \leq 3 \][/tex]
Therefore, the correct answer is:
d. [tex]\(-2 \leq x \leq 3\)[/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.