To solve the problem, we need to find the solution set for both equations: \(2x - 3 = 5\) and \(5x + 3 > -12\).
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Solve the equation \(2x - 3 = 5\): \[ 2x - 3 = 5 \] Add 3 to both sides: \[ 2x = 8 \] Divide by 2: \[ x = 4 \]
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Solve the inequality \(5x + 3 > -12\): \[ 5x + 3 > -12 \] Subtract 3 from both sides: \[ 5x > -15 \] Divide by 5: \[ x > -3 \]
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Combine the results:
- From the first equation, we have \(x = 4\).
- From the inequality, we have \(x > -3\).
Since \(x = 4\) satisfies the inequality \(x > -3\), the solution set includes \(x = 4\).
Thus, the complete solution set can be expressed as: \[ { 4 } \]
In conclusion, the solution set for the given equations is \({ 4 }\).
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