Get detailed and reliable answers to your questions on IDNLearn.com. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.
Sagot :
To solve the inequality [tex]\(4b + 8(2 - b) \leq 6b - 4\)[/tex], let's go step-by-step.
1. Expand and simplify both sides of the inequality:
[tex]\[4b + 8(2 - b) \leq 6b - 4\][/tex]
Expand [tex]\(8(2 - b)\)[/tex]:
[tex]\[4b + 16 - 8b \leq 6b - 4\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[4b - 8b + 16 \leq 6b - 4\][/tex]
[tex]\[ -4b + 16 \leq 6b - 4\][/tex]
3. Let's isolate the variable [tex]\(b\)[/tex] on one side of the inequality:
Add [tex]\(4b\)[/tex] to both sides to get all terms involving [tex]\(b\)[/tex] on the right-hand side:
[tex]\[16 \leq 10b - 4\][/tex]
4. Next, isolate the constant term on one side:
Add [tex]\(4\)[/tex] to both sides:
[tex]\[16 + 4 \leq 10b\][/tex]
[tex]\[20 \leq 10b\][/tex]
5. Now solve for [tex]\(b\)[/tex]:
Divide both sides by [tex]\(10\)[/tex]:
[tex]\[2 \leq b\][/tex]
or
[tex]\[b \geq 2\][/tex]
6. Write the solution set in interval notation:
The inequality [tex]\(b \geq 2\)[/tex] can be written in interval notation as:
[tex]\[[2, \infty)\][/tex]
So, the solution to the inequality [tex]\(4b + 8(2 - b) \leq 6b - 4\)[/tex] is [tex]\(b \in [2, \infty)\)[/tex].
1. Expand and simplify both sides of the inequality:
[tex]\[4b + 8(2 - b) \leq 6b - 4\][/tex]
Expand [tex]\(8(2 - b)\)[/tex]:
[tex]\[4b + 16 - 8b \leq 6b - 4\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[4b - 8b + 16 \leq 6b - 4\][/tex]
[tex]\[ -4b + 16 \leq 6b - 4\][/tex]
3. Let's isolate the variable [tex]\(b\)[/tex] on one side of the inequality:
Add [tex]\(4b\)[/tex] to both sides to get all terms involving [tex]\(b\)[/tex] on the right-hand side:
[tex]\[16 \leq 10b - 4\][/tex]
4. Next, isolate the constant term on one side:
Add [tex]\(4\)[/tex] to both sides:
[tex]\[16 + 4 \leq 10b\][/tex]
[tex]\[20 \leq 10b\][/tex]
5. Now solve for [tex]\(b\)[/tex]:
Divide both sides by [tex]\(10\)[/tex]:
[tex]\[2 \leq b\][/tex]
or
[tex]\[b \geq 2\][/tex]
6. Write the solution set in interval notation:
The inequality [tex]\(b \geq 2\)[/tex] can be written in interval notation as:
[tex]\[[2, \infty)\][/tex]
So, the solution to the inequality [tex]\(4b + 8(2 - b) \leq 6b - 4\)[/tex] is [tex]\(b \in [2, \infty)\)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.