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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]
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