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(a)
Draw a picture to represent this situation.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 2STP
The right side must be down than the right side
Explanation of Solution
Given:
In a balance have 12 pounds on the left side and 18 pounds on the right side.
Concept Used:
As 12 lbs is less than 18 lbs. So the right side must be down than the right side.
Thus, the right side must be down than the right side as 12 pounds on the left side and 18 pounds on the right side
(b)
Write an inequality.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 2STP
Explanation of Solution
Given:
In a balance have 12 pounds on the left side and 18 pounds on the tight side.
Concept Used:
Left side 12 lbs is less than the right side 18 lbs.
Inequality:
Calculation:
Inequality:
Thus, we can write the inequality
(c)
Create a table showing the result of doubling, tripling or quadrupling the weight of each side of the balance.
Create a second table showing the result of reducing the weight on each side of the balance by a factor of
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 2STP
Explanation of Solution
Given: In a balance have 12 pounds on the left side and 18 pounds on the tight side.
Concept Used:
Make two tables to represent the situation doubling, tripling or quadrupling the weight of each side of the balance and by a factor of
Calculation:
Create a table showing the result of doubling, tripling or quadrupling the weight of each side of the balance.
x | Original | 12 Pound | 18 Pound | |
x2 | Doubling | 24 Pound | < | 36 Pound |
x3 | Tripling | 36 Pound | < | 54 Pound |
x4 | Quadrupling | 48 Pound | < | 72 Pound |
Create a second table showing the result of reducing the weight on each side of the balance by a factor of
x | Original | 12 Pound | < | 18 Pound |
by a factor of | 6 Pound | < | 9 Pound | |
by a factor of | 4 Pound | < | 6 Pound | |
by a factor of | 3 Pound | < | 4.5 Pound |
Thus, the two tables represent the situations.
(d)
Describe the effect multiplying or dividing each side of an inequality by the same positive value has on the inequality.
(d)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given: In a balance have 12 pounds on the left side and 18 pounds on the tight side.
Concept Used:
If a true inequality is multiplied by a positive number, the resulting inequality is also true.
If a true inequality is divided by a positive number, the resulting inequality is also true.
Thus, if a true inequality is multiplied by a positive number, the resulting inequality is also true and if a true inequality is divided by a positive number, the resulting inequality is also true.
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