Answer :
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.
