To solve the inequalities separately, we first simplify them.
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For the first inequality: \[ x + 12 - 5x > 20 \] Combine like terms: \[ -4x + 12 > 20 \] Subtract 12 from both sides: \[ -4x > 8 \] Divide both sides by -4 (this reverses the inequality sign): \[ x < -2 \]
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For the second inequality: \[ x + 2 + 11x > 14 \] Combine like terms: \[ 12x + 2 > 14 \] Subtract 2 from both sides: \[ 12x > 12 \] Divide both sides by 12: \[ x > 1 \]
Now we combine the results of the two inequalities: \[ x < -2 \quad \text{or} \quad x > 1 \]
The solution can be expressed as a compound inequality: \[ (-\infty, -2) \cup (1, \infty) \]
In integer terms, the solution can be written as: \[ x < -2 \quad \text{or} \quad x > 1 \] So the integers satisfying this are: \[ { \ldots, -4, -3 } \cup { 2, 3, 4, \ldots } \]
Thus, the final solution in integer form is \( x < -2 \) or \( x > 1 \).