To find the solution set of the equations \(2x - 3 = 5\) and the inequality \(5x + 3 > -12\), we will solve each one separately and then find the intersection of their solutions.
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Solve the equation \(2x - 3 = 5\):
\[ 2x - 3 = 5 \] Add 3 to both sides: \[ 2x = 5 + 3 \] \[ 2x = 8 \] Divide by 2: \[ x = 4 \]
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Solve the inequality \(5x + 3 > -12\):
\[ 5x + 3 > -12 \] Subtract 3 from both sides: \[ 5x > -12 - 3 \] \[ 5x > -15 \] Divide by 5 (and since 5 is a positive number, the inequality remains the same): \[ x > -3 \]
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Combine the solutions:
The solution to the equation \(2x - 3 = 5\) gives us \(x = 4\). The solution to the inequality \(5x + 3 > -12\) gives us \(x > -3\).
Since \(x = 4\) satisfies \(x > -3\), the combined solution set is simply \(x = 4\).
Final Answer: The solution set is \({4}\).
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