Step 1 :First, we will solve \(5x + 2 = -8\). To solve for \(x\), we can subtract 2 from both sides and then divide the resulting equation by 5.
Step 2 :\(5x = -10\)
Step 3 :\(x = -2\)
Step 4 :For the second equation \((x + 2)(2x - 1) = 0\), we can solve for \(x\) by setting each factor equal to zero.
Step 5 :\(x + 2 = 0\) or \(2x - 1 = 0\)
Step 6 :\(x = -2\) or \(x = \frac{1}{2}\)
Step 7 :For the third equation \(\frac{3x}{x - 2} = \frac{3x + 10}{x}\), we can solve for \(x\) by cross multiplying and then simplifying the resulting equation.
Step 8 :\(3x^2 = (3x + 10)(x - 2)\)
Step 9 :\(3x^2 = 3x^2 - 6x + 10x - 20\)
Step 10 :\(-16x = -20\)
Step 11 :\(x = \frac{5}{4}\)
Step 12 :For the fourth equation \(\frac{2}{3}x + 5 = -7\), we can solve for \(x\) by subtracting 5 from both sides and then multiplying the resulting equation by \(\frac{3}{2}\).
Step 13 :\(\frac{2}{3}x = -12\)
Step 14 :\(x = -18\)
Step 15 :For the fifth inequality \(3x + 2 > 8\), we can find the values of \(x\) that satisfy the inequality by subtracting 2 from both sides and then dividing the resulting inequality by 3.
Step 16 :\(3x > 6\)
Step 17 :\(x > 2\)