To solve the inequality \( ax - 3 < 17 \), follow these steps:
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Add 3 to both sides of the inequality: \[ ax < 17 + 3 \] \[ ax < 20 \]
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Now, divide both sides by \( a \). Note that the direction of the inequality will change if \( a < 0 \):
- If \( a > 0 \): \[ x < \frac{20}{a} \]
- If \( a < 0 \): \[ x > \frac{20}{a} \]
- If \( a = 0 \), the inequality \( -3 < 17 \) is always true, meaning \( x \) can be any real number.
So, the solution to the inequality depends on the value of \( a \):
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If \( a > 0 \): \[ x < \frac{20}{a} \]
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If \( a < 0 \): \[ x > \frac{20}{a} \]
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If \( a = 0 \): \[ x \text{ is any real number.} \]