Tutorial 2: More Algebra, Inequalities and Absolute values
CHECK THE LINK BELOW THIS HEADING FOR SOLUTIONS! Remember to check the corresponding Questions on the memo only Click here to view the solutions to the question below 1. Solve the equation (a) \(\frac{1}{t-1} + \frac{t}{3} = \frac{1}{3}\) (b) \(\frac{1}{x} = \frac{4}{3x} + 1\) (c) \(\frac{z}{5} = \frac{3}{10}z + 7\) (d) \(r-2[1-3(2r+4)] = 61\) (e) \((t-4)^{2} = (t+4)^{2} + 32\) (f) \(\frac{2}{3}x - \frac{1}{4} = \frac{1}{6}x - \frac{1}{9}\) (g) \(\frac{4}{x-1} + \frac{2}{x + 1} = \frac{35}{x^2 - 1}\) (h) \((\frac{1}{x-1} 2 \frac{2}{x^2}\) (i) \(\sqrt{2x + 1} + 1 = x\) (j) \(\sqrt{\sqrt{x-5}+x} = 5\) (k) \(4(x + 1)^{\frac{1}{2}} - 5(x + 1)^{\frac{3}{2}} + (x + 1)^{\frac{5}{2}} = 0\) 2. Solve the inequality. Express the solution in interval form and illustrate the solution set on the real number line. (a) \(4-3x \leq -(1+8x)\) (b) \( \frac{2x+1}{x-5} \leq 3\) (c) \( \frac{(x-1)^2}{(x+1)(x+3)}\) (d) \...