To find the solution set for the equations \( 2x - 3 = 5 \) and \( 5x + 3 > -12 \), we will solve each inequality separately.
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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: The solution to \( 2x - 3 = 5 \) gives us \( x = 4 \), and the solution to \( 5x + 3 > -12 \) gives us \( x > -3 \).
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Determine the overall solution set: Since \( 4 > -3 \), the solution set for both conditions is \( x \) must be both \( 4 \) (from the equality) and greater than \(-3\) (from the inequality). Since the equality provides a specific value, the solution set is \( x = 4 \).
Thus, the solution set is: \[ { x = 4 } \]