Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Sure! Let's solve the inequality step-by-step:
1. Start with the given inequality:
[tex]\[ -3x + 12 \geq 7x - 8 \][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the inequality and the constant terms to the other side. To do this, subtract [tex]\(7x\)[/tex] from both sides:
[tex]\[ -3x - 7x + 12 \geq -8 \][/tex]
3. Combine like terms:
[tex]\[ -10x + 12 \geq -8 \][/tex]
4. Next, move the constant term on the left side to the right side by subtracting 12 from both sides:
[tex]\[ -10x + 12 - 12 \geq -8 - 12 \][/tex]
5. Combine the constants:
[tex]\[ -10x \geq -20 \][/tex]
6. Finally, isolate [tex]\(x\)[/tex] by dividing both sides of the inequality by [tex]\(-10\)[/tex]. Here, dividing by a negative number will reverse the inequality direction:
[tex]\[ x \leq 2 \][/tex]
So, the solution to the inequality is:
[tex]\[ x \leq 2 \][/tex]
This means that all [tex]\(x\)[/tex] values less than or equal to 2 satisfy the inequality. Therefore, the solution in interval notation is:
[tex]\[ (-\infty, 2] \][/tex]
1. Start with the given inequality:
[tex]\[ -3x + 12 \geq 7x - 8 \][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the inequality and the constant terms to the other side. To do this, subtract [tex]\(7x\)[/tex] from both sides:
[tex]\[ -3x - 7x + 12 \geq -8 \][/tex]
3. Combine like terms:
[tex]\[ -10x + 12 \geq -8 \][/tex]
4. Next, move the constant term on the left side to the right side by subtracting 12 from both sides:
[tex]\[ -10x + 12 - 12 \geq -8 - 12 \][/tex]
5. Combine the constants:
[tex]\[ -10x \geq -20 \][/tex]
6. Finally, isolate [tex]\(x\)[/tex] by dividing both sides of the inequality by [tex]\(-10\)[/tex]. Here, dividing by a negative number will reverse the inequality direction:
[tex]\[ x \leq 2 \][/tex]
So, the solution to the inequality is:
[tex]\[ x \leq 2 \][/tex]
This means that all [tex]\(x\)[/tex] values less than or equal to 2 satisfy the inequality. Therefore, the solution in interval notation is:
[tex]\[ (-\infty, 2] \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.