Polynomial and rational equations and inequalities

Solve the equation

$$3(x-2)+5=2(x+1)-1.$$

Solution available to those who have unlocked the subject.

Solve the equations

$$x^2-7x+10=0\text{and}2x^2+5x-3=0.$$

Solution available to those who have unlocked the subject.

Solve the equations

$$5x^2-20=0\text{and}3x^2+7x=0.$$

Solution available to those who have unlocked the subject.

Solve the equations

$$9x^2-6x+1=0\text{and}{x}^2-3x+5=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$x^2-7x+12=0$$

using the sum and product of the roots, and factor the trinomial.

Solution available to those who have unlocked the subject.

Solve the equation

$$x^3-9x=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$x^3-7x+6=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$x^3+3x^2-4x-12=0.$$

Solution available to those who have unlocked the subject.

Solve the equations

$$x^4-10x^2+9=0\text{and}{x}^4-3x^2-4=0.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$$2(1-x)\ge x-4.$$

Solution available to those who have unlocked the subject.

Solve the inequalities

$$x^2-4x+3>0\text{and}-x^2+x+6\ge 0.$$

Solution available to those who have unlocked the subject.

Solve the inequalities

$$x^2-6x+9>0\text{and}{x}^2+2x+2<0.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$$x^3-x\le 0.$$

Solution available to those who have unlocked the subject.

Solve the inequality and the system

$$\frac{x+2}{x-3}\le 0\text{and}\{\begin{array}{l}{x}^2-4\le 0\\ 2x+1>0\end{array}$$

Solution available to those who have unlocked the subject.