To solve the system of equations and inequalities given by \(2x - 3 = 5\) and \(5x + 3 > -12\), we'll tackle each part separately.
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Solve the equation \(2x - 3 = 5\):
\[ 2x - 3 = 5 \] Adding 3 to both sides: \[ 2x = 8 \] Dividing by 2: \[ x = 4 \]
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Solve the inequality \(5x + 3 > -12\):
\[ 5x + 3 > -12 \] Subtracting 3 from both sides: \[ 5x > -15 \] Dividing by 5: \[ x > -3 \]
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Combine the solutions:
From the equation, we have \(x = 4\), and from the inequality, we derived \(x > -3\). Now we want to see if the solution to the equation meets the criteria of the inequality:
Since \(4 > -3\), the solution \(x = 4\) satisfies the inequality.
Therefore, the solution set of the system is:
\[ {4} \]
Since both the value \(x = 4\) meets the condition \(x > -3\), the solution set for the system of equations and inequalities is \(x = 4\).