Chapter 2

Without performing any calculations, match the inequality with its solution. Explain your reasoning. (a) \(2 x \leq-6\) (b) \(-2 x \leq 6\) (c) \(|x+2| \leq 6\) (d) \(|x+2| \geq 6\) (i) \(x \leq-8\) or \(x \geq 4\) (ii) \(x \geq-3\) (iii) \(-8 \leq x \leq 4\) (iv) \(x \leq-3\)

Match the equation with a method you would use to solve it. Explain your reasoning. (Use each method once and do not solve the equations.) (a) \(3 x^{2}+5 x-11=0 \quad\) (i) Factoring (b) \(x^{2}+10 x=3 \quad\) (ii) Extracting square roots (c) \(x^{2}-16 x+64=0 \quad\) (iii) Completing the square (d) \(x^{2}-15=0 \quad\) (iv) Quadratic Formula

Find the inverse function. $$y=12 x$$

Completely factor the expression over the real numbers. $$x^{5}-27 x^{2}$$

Find the inverse function. $$y=5 x+8$$

Completely factor the expression over the real numbers. $$x^{3}-5 x^{2}-14 x$$

Find the inverse function. $$y=x^{3}+7$$

Completely factor the expression over the real numbers. $$x^{3}+5 x^{2}-2 x-10$$

Find the inverse function. $$y=\sqrt[3]{x-7}$$

Completely factor the expression over the real numbers. $$5(x+5) x^{1 / 3}+4 x^{4 / 3}$$