Let’s break down the inequality step by step to find the second step in solving:
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Start with the given inequality: \[ -(3x+3)-2x>-4(x-2)-2 \]
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First Step: Use the Distributive Property to simplify both sides of the inequality:
- Left side: \(-3x - 3 - 2x\)
- Right side: \(-4x + 8 - 2\)
Rewriting it, we get: \[ -3x - 3 - 2x > -4x + 6 \]
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Combine Like Terms: \[ -5x - 3 > -4x + 6 \]
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Now, the next step usually involves isolating the variable on one side of the inequality, which could be using either the Addition Property of Inequality (to get terms involving \(x\) on one side) or the Division Property of Inequality if we need to divide.
So, to answer the question, the second step in solving the inequality after the initial application of the Distributive Property would be:
Combine Like Terms.
Now, to address the second part of your question regarding the inequalities:
- The expression \(y < mx + b\) indicates a linear function, typically in slope-intercept form.
- The inequality \(ax + by ≤ c\) is a linear inequality that represents a region in the coordinate plane.
If you're solving for \(y\) in \(ax + by ≤ c\), you would typically isolate \(y\), giving you \(by ≤ -ax + c\) or \(y ≤ (-a/b)x + (c/b)\), which is in slope-intercept form.