Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Let's solve the given inequality step-by-step and identify the property used in each step.
### Given Inequality:
[tex]\[ 5x - 9 < 91 \][/tex]
### Step-by-Step Solution:
1. Original Inequality:
[tex]\[ 5x - 9 < 91 \][/tex]
2. Isolating the term involving [tex]\( x \)[/tex]:
To isolate the term [tex]\( 5x \)[/tex] on the left side of the inequality, we need to eliminate the [tex]\(-9\)[/tex]. We achieve this by adding 9 to both sides of the inequality:
[tex]\[ 5x - 9 + 9 < 91 + 9 \][/tex]
This simplifies to:
[tex]\[ 5x < 100 \][/tex]
- Property Used: This step uses the Addition Property which states that adding the same number to both sides of an inequality will not change the direction of the inequality.
3. Solving for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we divide both sides of the inequality by 5:
[tex]\[ \frac{5x}{5} < \frac{100}{5} \][/tex]
This simplifies to:
[tex]\[ x < 20 \][/tex]
- Property Used: This step uses the Multiplication Property of inequality (specifically, division is a form of multiplication by the reciprocal), which states that dividing both sides of an inequality by a positive number does not change the direction of the inequality.
### Conclusion:
The property used in the second step of solving the inequality [tex]\( 5x - 9 < 91 \)[/tex] leading to [tex]\( 5x < 100 \)[/tex] is the Addition Property.
### Given Inequality:
[tex]\[ 5x - 9 < 91 \][/tex]
### Step-by-Step Solution:
1. Original Inequality:
[tex]\[ 5x - 9 < 91 \][/tex]
2. Isolating the term involving [tex]\( x \)[/tex]:
To isolate the term [tex]\( 5x \)[/tex] on the left side of the inequality, we need to eliminate the [tex]\(-9\)[/tex]. We achieve this by adding 9 to both sides of the inequality:
[tex]\[ 5x - 9 + 9 < 91 + 9 \][/tex]
This simplifies to:
[tex]\[ 5x < 100 \][/tex]
- Property Used: This step uses the Addition Property which states that adding the same number to both sides of an inequality will not change the direction of the inequality.
3. Solving for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we divide both sides of the inequality by 5:
[tex]\[ \frac{5x}{5} < \frac{100}{5} \][/tex]
This simplifies to:
[tex]\[ x < 20 \][/tex]
- Property Used: This step uses the Multiplication Property of inequality (specifically, division is a form of multiplication by the reciprocal), which states that dividing both sides of an inequality by a positive number does not change the direction of the inequality.
### Conclusion:
The property used in the second step of solving the inequality [tex]\( 5x - 9 < 91 \)[/tex] leading to [tex]\( 5x < 100 \)[/tex] is the Addition Property.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.