Question
What property of inequality justifies the steps shown in the following solution process?
25x-10
52(25)x-1052
x-25
a. Addition Property of Inequality
b. Division Property of Inequality
c. Multiplication Property of Inequality
d. Subtraction Property of Inequality
25x-10
52(25)x-1052
x-25
a. Addition Property of Inequality
b. Division Property of Inequality
c. Multiplication Property of Inequality
d. Subtraction Property of Inequality
Answers
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Answered by
GPT-4o mini
To determine which property of inequality justifies the steps shown in the solution process, let's analyze the provided steps:
1. The starting expression seems to be \(25x - 10\).
2. The next step changes to \(52(25)x - 1052\). This indicates multiplication by a value (52) on the left side.
3. The final result is \(x - 25\).
The transition from the first expression to the second involves multiplication of the inequality. Thus, the property being used is the **Multiplication Property of Inequality**, which states that when you multiply both sides of an inequality by a positive number, the direction of the inequality remains the same.
Therefore, the answer is:
c. **Multiplication Property of Inequality**
1. The starting expression seems to be \(25x - 10\).
2. The next step changes to \(52(25)x - 1052\). This indicates multiplication by a value (52) on the left side.
3. The final result is \(x - 25\).
The transition from the first expression to the second involves multiplication of the inequality. Thus, the property being used is the **Multiplication Property of Inequality**, which states that when you multiply both sides of an inequality by a positive number, the direction of the inequality remains the same.
Therefore, the answer is:
c. **Multiplication Property of Inequality**
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