Question

У нас есть система Можно ли Домножать, делить, прибавлять, вычислять на одно число обе части одного из этих уравнений не делая это с другим? Выйдет верное равенство? Очень не уверен насчёт вычитать и складывать. Помогите.

Answer 1

Можно прибавлять отнимать умножать и делить обе части уравнения на одно и тоже число.При этом получается равносильное уравнение.

Answer 2

Solving Equations by Performing Operations on One Side

When solving equations, you can perform operations on one side of the equation without necessarily doing the same operations on the other side. Let's break down the different operations you can perform on one side of an equation:

1. Multiplication: - You can multiply both sides of an equation by the same number without affecting the equality of the equation. For example, if you have the equation 2x = 6, you can multiply both sides by 3 to get 6x = 18.

2. Division: - Similarly, you can divide both sides of an equation by the same non-zero number without changing the equality. For instance, if you have the equation 4y = 16, you can divide both sides by 4 to get y = 4.

3. Addition and Subtraction: - Adding or subtracting the same number from both sides of an equation preserves the equality. For example, if you have the equation z + 5 = 12, you can subtract 5 from both sides to get z = 7.

4. Exponents and Roots: - Raising both sides of an equation to the same power or taking the same root of both sides maintains the equality. For instance, if you have the equation 3^x = 27, you can take the logarithm of both sides to solve for x.

In summary, you can perform these operations on one side of an equation without necessarily doing the same operations on the other side, as long as you maintain the equality of the equation.

If you have specific equations or operations in mind, feel free to provide more details for a more tailored explanation!