To solve addition inequalities, you essentially follow the same principles as solving regular inequalities, but apply the operations carefully. Here’s a quick guide on how to approach it:
Steps to Solve Addition Inequalities:
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Understanding the Inequality: An inequality might look like this: \[ x + a < b \] or \[ x + a \geq b \]
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Isolate the Variable: To solve for \( x \), you will subtract \( a \) from both sides: \[ x < b - a \] or \[ x \geq b - a \]
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Write the Solution: Depending on whether the inequality is strict (<) or non-strict (≥), you'll have different types of solution sets:
- For \( x < b - a \), the solution is all numbers less than \( b - a \).
- For \( x \geq b - a \), the solution includes \( b - a \) and all greater numbers.
Example Problems
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Example 1: Solve \( x + 5 < 10 \)
- Subtract 5 from both sides: \[ x < 10 - 5 \] \[ x < 5 \]
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Example 2: Solve \( x + 3 \geq 7 \)
- Subtract 3 from both sides: \[ x \geq 7 - 3 \] \[ x \geq 4 \]
Conclusion
Solving addition inequalities is straightforward: isolate the variable by performing the same operation on both sides while respecting the inequality sign. For any specific problems or more complex cases, feel free to ask for detailed assistance!
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