IDNLearn.com offers a comprehensive platform for finding and sharing knowledge. Join our Q&A platform to get accurate and thorough answers to all your pressing questions.
Sagot :
To solve the given inequality:
[tex]\[ -4(x+7) < 3(x-2) \][/tex]
we will proceed step-by-step to derive the equivalent inequality.
1. Distribute the constants within the parentheses:
[tex]\[ -4(x + 7) < 3(x - 2) \][/tex]
[tex]\[ -4x - 28 < 3x - 6 \][/tex]
2. Combine like terms by adding [tex]\(4x\)[/tex] to both sides:
[tex]\[ -28 < 3x - 6 + 4x \][/tex]
[tex]\[ -28 < 7x - 6 \][/tex]
3. Add 6 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ -28 + 6 < 7x \][/tex]
[tex]\[ -22 < 7x \][/tex]
4. Divide both sides by 7 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{-22}{7} < x \][/tex]
[tex]\[ x > \frac{-22}{7} \][/tex]
5. To express the result in a form that matches the given multiple-choice answers, we can reverse the inequality and terms, yielding:
[tex]\[ 7x > -22 \][/tex]
or in other terms:
[tex]\[ -7x < 22 \][/tex]
Therefore, the equivalent inequality is:
[tex]\[ \boxed{-7x < 22} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
[tex]\[ -4(x+7) < 3(x-2) \][/tex]
we will proceed step-by-step to derive the equivalent inequality.
1. Distribute the constants within the parentheses:
[tex]\[ -4(x + 7) < 3(x - 2) \][/tex]
[tex]\[ -4x - 28 < 3x - 6 \][/tex]
2. Combine like terms by adding [tex]\(4x\)[/tex] to both sides:
[tex]\[ -28 < 3x - 6 + 4x \][/tex]
[tex]\[ -28 < 7x - 6 \][/tex]
3. Add 6 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ -28 + 6 < 7x \][/tex]
[tex]\[ -22 < 7x \][/tex]
4. Divide both sides by 7 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{-22}{7} < x \][/tex]
[tex]\[ x > \frac{-22}{7} \][/tex]
5. To express the result in a form that matches the given multiple-choice answers, we can reverse the inequality and terms, yielding:
[tex]\[ 7x > -22 \][/tex]
or in other terms:
[tex]\[ -7x < 22 \][/tex]
Therefore, the equivalent inequality is:
[tex]\[ \boxed{-7x < 22} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thanks for visiting IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more helpful information.