Question
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Tutor-Verified Answer
Answer
\( x < 1 \)
Solution
1. Write the inequality:
\[
5(x-1) > 7(x-1)
\]
2. Subtract \(7(x-1)\) from both sides:
\[
5(x-1) - 7(x-1) > 0
\]
3. Factor out the common term \((x-1)\):
\[
(x-1)(5-7) > 0
\]
4. Simplify the constant factor \(5-7\):
\[
(x-1)(-2) > 0
\]
5. Divide both sides by \(-2\). Remember to reverse the inequality symbol when dividing by a negative number:
\[
x-1 < 0
\]
6. Solve for \(x\) by adding 1 to both sides:
\[
x < 1
\]
The solution to the inequality is:
\[
x < 1
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To solve the inequality \( 5(x-1) > 7(x-1) \), start by expanding both sides: \( 5x - 5 > 7x - 7 \). Next, bring similar terms together by subtracting \( 5x \) from both sides: \( -5 > 2x - 7 \). Then, add \( 7 \) to both sides to isolate the term with \( x \): \( 2 > 2x \). Finally, divide both sides by \( 2 \): \( 1 > x \) or \( x < 1 \). This means that any value of \( x \) less than \( 1 \) will satisfy the inequality—simple as pie! Just remember, when you multiply or divide by a negative number, you must flip the inequality sign. Keep that in your back pocket for your next math adventure!
