To find the solution set for the two equations \(2x - 3 = 5\) and \(5x + 3 > -12\), we'll solve each one step by step.
-
Solve the equation \(2x - 3 = 5\): \[ 2x - 3 = 5 \] Add 3 to both sides: \[ 2x = 8 \] Divide both sides by 2: \[ x = 4 \]
-
Solve the inequality \(5x + 3 > -12\): \[ 5x + 3 > -12 \] Subtract 3 from both sides: \[ 5x > -15 \] Divide both sides by 5: \[ x > -3 \]
-
Combine the solutions: The solution to the first equation gives \(x = 4\). The solution to the inequality gives \(x > -3\). Since \(4 > -3\), \(x = 4\) satisfies the inequality.
Thus, the solution set for the system of equations and inequalities is: \[ {4} \]