Let's solve the inequalities one by one:
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For the inequality \(10x < 40\): \[ x < \frac{40}{10} \] \[ x < 4 \]
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For the inequality \(-10y < 40\): To isolate \(y\), we first divide both sides by \(-10\). Remember that when you divide by a negative number, you flip the inequality sign: \[ y > \frac{40}{-10} \] \[ y > -4 \]
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For the inequality \(10z < -40\): \[ z < \frac{-40}{10} \] \[ z < -4 \]
So the solutions to the inequalities are:
- \(x < 4\)
- \(y > -4\)
- \(z < -4\)