A selection of free mathematics resources (calculators, exercises, games, quizzes, course reminders) that help you learn to solve equations algebraically.

An **equation is an equality that involves one or more variables**, solving an equation in a set is to find the value or values of the variables in that set that verify the equation,
these are the solutions of the equation. The variables are often referred to as the unknown,
when the equation has only one unknown, it is often referred to as x.

For example, 3x-3=0 is an equation, solving for x in ℝ this equation is to find the solutions in ℝ of this equation.

When we have to solve several equations, with several variables, we speak of a system of equations.

There are **methods and formulas for solving certain types of equations** such as first degree equations (linear equation),
second degree equations (quadratic equation), or product equations.

### Solve an equation with one unknown of the first degree

- When we add or subtract the same real to both members of an equation, we obtain a new equation which has the same solutions as the previous one.
- When we multiply or divide the two members of an equation by a non-zero real, we obtain a new equation that has the same solutions as the previous one.
### Solving a product equation

- Saying that a.b = 0 is equivalent to saying that a is zero or that b is zero.
- Think of using the special expansions to get back to a product of factors and a classic case of solving an equation.
### Solve a second degree equation using the discriminant

- When `Delta<0` the equation has no root
- When `Delta=0` the equation has a root `-b/2a`
- When `Delta>0` the equation has two distinct roots `(-b-sqrt(Delta))/(2a)` and `(-b+sqrt(Delta))/(2a)`

**Solving an equation with one unknown** x in R, it is to determine the set of real numbers x verifying the said equation.
This set is called the set of solutions of the equation.

A product of two factors is zero if and only if one of the factors is zero.

We call the discriminant of the trinomial `a*x^2+b*x+c`, with a not zero, the real `Delta=b^2-4*a*c`.

- arithmetic_solver : countdown solver. This countdown solver allows finding a target number from a set of integer in using arithmetic operations.
- complexe_solve : solving quadratic equation with complex number. The complex number equation calculator returns the complex values for which the quadratic equation is zero.
- discriminant : calculation of the discriminant online. Calculator that allows the calculation of the discriminant of a quadratic equation online.
- equation_solver : solve for x calculator. The equation solver allows to solve equations with an unknown with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.
- equation_straight_line : find equation of a straight line from two points. The equation straight line calculator allows to calculate the equation of a straight line from the coordinates of two points with step by step calculation.
- equation_tangent_line : Find the equation of tangent line. The tangent line equation calculator is used to calculate the equation of tangent line to a curve at a given abscissa point with stages calculation.
- inequality_solver : inequality calculator. Inequality solver that solves an inequality with the details of the calculation: linear inequality, quadratic inequality.
- pythagorean : Pythagorean theorem calculator. The calculator uses the Pythagorean theorem to verify that a triangle is right-angled or to find the length of one side of a right-angled triangle.
- solve_equations : solve system of linear equations. The solver of systems of linear equations allows to solve equations with several unknowns: system of equations with 2 unknowns, system of equations with 3 unknowns, system with n unknowns.

- Quiz solving equations with one unknown (equations): This quiz on equations allows to practice solving different types of equations with one unknown.
- Quiz solving first degree equations (equations): This quiz on first degree equations allows to practice solving simple equations with one unknown.
- Quiz solving equations of the second degree (equations): This quiz on the equations of the second degree allows to practice the methods of resolution based on the use of the discriminant.

- Exercise 1119, introduction to solving equations - introduction to equation solving - equations : The objective of this activity is to complete a "hole" operation, otherwise known as solving a simple equation.
- Exercise 1336, first degree equation with one unknown of the form ax+b=c - solving equations - algebraic calculus - equations : The purpose of this exercise is to solve a linear equation of the first degree with one unknown of the form ax+b=c.
- Exercise 1337, equation of the first degree with one unknown form x+b=c - solving equations - algebraic calculus - equations : The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form x+b=c.
- Exercise 1338, equation of the first degree with one unknown form ax+b=cx+d - solving equations - algebraic calculus - equations : The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form ax+b=cx+d.
- Exercise 1339, solving an equation written in natural language - solving equations - algebraic calculus - equations : The purpose of this corrected math exercise is to solve an equation written in natural language.
- Exercise 1340, equations and percentages - solving equations - algebraic calculus - equations : The purpose of this exercise is to solve a numerical problem by calculating the percentage of a whole number.
- Exercise 1341, calculation of a percentage from two numbers - solving equations - algebraic calculus - equations : The purpose of this math exercise is to calculate a percentage from two numbers.
- Exercise 1342, calculation of a percentage from two given integers - solving equations - algebraic calculus - equations : The purpose of this math exercise is to determine a percentage from two given integers.
- Exercise 1422, solve an inequation of the first degree - solving equations and inequations of the first degree : The objective of this corrected math exercise is to solve a first order inequation.
- Exercise 1423, solve a system of two equations with two unknowns - solving equations and inequations of the first degree - equations of lines and linear systems - equations : The objective of this corrected math exercise is to solve a system of two equations with two unknowns.
- Exercise 1438, factoring, developing, simplifying and solving - mathematics exams and competitions - expansion of algebraic expressions - solving equations and inequations of the first degree - factoring - equations : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.
- Exercise 1439, factoring, developing, simplifying and solving - mathematics exams and competitions - expansion of algebraic expressions - solving equations and inequations of the first degree - factoring - equations : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.
- Exercise 1440, equating and solving a problem - mathematics exams and competitions - solving equations and inequations of the first degree - equations : The objective of this exercise is to equate a problem in order to solve it.
- Exercise 1441, using a system of equations to solve a problem - mathematics exams and competitions - equations of lines and linear systems - equations : The purpose of this exercise is to use a system of two equations with two unknowns to solve a problem.
- Exercise 1501, 1st degree equations - solving equations - equations : This corrected exercise allows to practice solving linear equations with one unknown of the form ax+b=0.
- Exercise 1502, 2nd degree equations - solving equations - equations : The purpose of this exercise on quadratic equations is to practice solving 2nd degree equations and null product equations.
- Exercise 1503, 2nd degree and first degree equations - solving equations - equations : The purpose of this exercise is to solve a second degree equation by reducing it to solving a first degree equation.
- Exercise 1504, null product equations - solving equations - equations : The goal of this exercise is to solve a null product equation of the type a*b=0, with a=0 or b=0.
- Exercise 1508, solve graphically an equation - solving equations - square and inverse functions - equations : The purpose of this exercise is to solve graphically an equation.
- Exercise 1511, absolute value of a numerical expression - order, absolute value, inequations : This corrected exercise consists simply in calculating the absolute value of a numerical expression.
- Exercise 1512, absolute value of a fraction - order, absolute value, inequations : This corrected exercise consists simply in calculating the absolute value of an algebraic expression composed of fractions.
- Exercise 1513, equation with absolute value - order, absolute value, inequations - equations : The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form |x-a|=b).
- Exercise 1514, equation with absolute value - order, absolute value, inequations - equations : The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form |x-a|=b).
- Exercise 1601, discriminant of a polynomial - second degree polynomials - solving equations : The goal of this corrected exercise is to calculate the discriminant of a second degree polynomial from its algebraic form.
- Exercise 1602, discriminant and number of solution of a quadratic equation - equations - second degree polynomials - solving equations : The purpose of this corrected exercise is to find the number of solution of a second degree equation as a function of the discriminant.
- Exercise 1603, solutions of a second degree equation - equations - second degree polynomials - solving equations : The purpose of this corrected exercise is to use the discriminant of a second degree equation to find its roots.
- Exercise 2411, calculate from the coordinates of a point the equation of a line passing through the origin - linear functions and affine functions - equations of lines and linear systems - equations : The purpose of this exercise is to find the equation of a line representing a linear function that passes through a given point.
- Exercise 2413, calculate the equation of a line from the coordinates of two points - linear functions and affine functions - equations of lines and linear systems - equations : The purpose of this exercise is to find the equation of a line from two points.
- Exercise 24121, graphical reading of the image of a number by a function - linear functions and affine functions : The purpose of this exercise is to read on a graph the image of a number by a function.
- Exercise 24122, graphical reading of the antecedent of a number by a function - linear functions and affine functions : The purpose of this exercise is to read on a graph the antecedent by a function of a number.

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