24. Solving equations and inequalities

The resolution of equations and inequalities is one of the most important topics in the complete Mathematics course for the Enem test. This topic covers a wide range of concepts and techniques that are fundamental to solving complex mathematical problems. Additionally, understanding these concepts is crucial to success in other areas of mathematics, such as geometry, trigonometry, and advanced algebra.

Equations

An equation is a mathematical statement that states that two expressions are equal. In other words, it is a mathematical sentence that asserts the equality of two expressions. The simplest equation we can have is a linear equation, which has the form ax + b = 0, where a and b are constants and x is the variable. To solve this equation, we need to find the value of x that makes the equality true.

To solve more complex equations, such as quadratic, cubic, or higher-degree equations, we can use a variety of techniques, such as factoring, the Sarrus rule, the Newton-Raphson method, and others. Each of these techniques has its own advantages and disadvantages, and choosing the appropriate technique depends on the specific type of equation we are trying to solve.

Inequalities

An inequality is similar to an equation, but instead of asserting that two expressions are equal, an inequality asserts that an expression is less than (<), greater than (>), less than or equal (<=), or greater or equal (>=) to another. Like equations, inequalities can be linear, quadratic, cubic, or higher, and solving inequalities involves finding the set of values ​​for the variable that makes the inequality true.

The main difference between solving equations and inequalities is that, while the solution of an equation is a specific number, the solution of an inequality is usually a range of numbers. For example, the solution of the inequality x > 2 is the set of all numbers greater than 2.

Resolving Equations and Inequalities in Enem

On Enem, students are often asked to solve equations and inequalities in a variety of contexts. For example, they might be asked to solve an equation to find the value of an unknown variable in a geometry problem, or they might be asked to solve an inequality to determine the range of possible values ​​for a variable in an optimization problem.< /p>

To succeed in these questions, students need to have a solid understanding of the concepts and techniques involved in solving equations and inequalities. This includes understanding how to manipulate equations and inequalities (for example, adding, subtracting, multiplying, or dividing both sides of an equation or inequality by a number), how to use the distributive property to expand or condense expressions, and how to use factoring techniques to simplify expressions.

In summary, solving equations and inequalities is a crucial topic in the complete Mathematics course for the ENEM exam. Mastering this topic will not only help students solve a wide range of math problems on the ENEM, but will also provide them with the skills they need to succeed in other areas of math.

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