To solve the inequality \((\frac{3}{4}) x + 10 > -1\), we'll start by isolating \(x\).
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Subtract \(10\) from both sides: \[ \frac{3}{4} x > -1 - 10 \]
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Simplifying the right side gives: \[ \frac{3}{4} x > -11 \]
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Now, multiply both sides by \(\frac{4}{3}\) (remember that since \(\frac{4}{3}\) is positive, the direction of the inequality does not change): \[ x > -11 \times \frac{4}{3} \]
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Calculating \(-11 \times \frac{4}{3}\): \[ -11 \times \frac{4}{3} = -\frac{44}{3} \]
So, we get: \[ x > -\frac{44}{3} \]
Now we will compare this result to the options given:
- \(x < 12\)
- \(x > 12\)
- \(x < -12\)
None of the provided options match the solution \(x > -\frac{44}{3}\) (which is approximately \(x > -14.67\)). However, it's clear that this means \(x\) is greater than a negative value, which does not match any of the inequalities listed.
Thus, the conclusion is that the provided options don't include the correct interpretation of the inequality solution.
To summarize: The correct solution is \(x > -\frac{44}{3}\) (approximately \(x > -14.67\)).
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