Find the set of values for $x$ which satisfies: $$5x + 12 \geq 2$$
$x \geq -2$
Find the set of values for $x$ which satisfies: $$12 - 3x \leq 6$$
$x \geq 2$
Find the set of values for $x$ which satisfies: $$7(x+3) - 2(3x-1) < 0$$
$x < -23$
Find the set of values for $x$ which satisfies: $$3(4x-1) - 5(x-3) < 9$$
$x < -\dfrac{3}{7}$
Find the set of values for $x$ which satisfies: $$x^2 - 4x + 3 < 0$$
$1 < x < 3$
Find the set of values for $x$ which satisfies: $$15 + 8x + x^2 < 0$$
$-5 < x < -3$
Find the set of values for $x$ which satisfies: $$x^2 + 2x \leq 8$$
$-4 \leq x \leq 2$
Find the set of values for $x$ which satisfies: $$x^2 - 4 \leq 0$$
$-2 \leq x \leq 2$
Find the set of values for $x$ which satisfies: $$x^2 - 6x + 5 > 0$$
$x < 1$ or $x > 5$
Find the set of values for $x$ which satisfies: $$x^2 + 4x > 12$$
$x < -6$ or $x > 2$
Find the set of values for $x$ which satisfies: $$2x^2 - 9x + 4 \leq 0$$
$\dfrac{1}{2} \leq x \leq 4$
Find the set of values for $x$ which satisfies: $$2x^2 + 9x - 5 > 0$$
$x < -5$ or $x > \dfrac{1}{2}$
Find the set of values for $x$ which satisfies: $$x^2 + 6 < 8x - 9$$
$3 < x < 5$
Find the set of values for $x$ which satisfies: $$x(2x+1) > x^2 + 6$$
$-3 < x < -2$
The equation $$2x^2 - kx + k = 0$$ has two real roots. Find the set of possible values for $k$.
$k < 0$ or $k > 8$
The equation $$x^2 + kx + 2k - 3 = 0$$ has no real roots. Find the set of possible values for $k$.
$2 < k < 6$
Solve the following inequality, giving your answer in set notation: $$(x-2)^2 \leq 2x - 1$$
$\{x: 1 \leq x \leq 5\}$
Solve the following inequality, giving your answer in set notation: $$2(13+2x) < (6+x)(1-x)$$
$\{x: -5 < x < -4\}$
Solve the following inequality, giving your answer in set notation: $$x(5-6x) < 3 - 4x$$
$\{x: x < \frac{1}{2} \} \cup \{x: x > 1\}$
Solve the following inequality, giving your answer in set notation: $$(x+2)(x+3) \geq 20$$
$\{x: x \leq -7 \} \cup \{x: x \geq 2\}$