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In algebra, one of the main tasks is to find the value of an unknown variable. To achieve this, isolating the variable becomes crucial. It essentially means rearranging an equation so that the variable stands alone on one side of the equation. In the equation \( y + 3 = -10 \), 'isolate the variable' refers to getting \( y \) by itself.

• First, identify the variable you need to isolate.
• Use inverse operations to move all other terms to the opposite side.

In this case, we subtract 3 from both sides of the equation to accomplish this, resulting in \( y = -10 - 3 \). The variable \( y \) is now isolated and ready for the next step, which is simplifying the right-hand side.

Simplifying an equation means making it as straightforward as possible. When faced with an equation like \(-1(y + 3) = 10 \), the first step is to remove any added complexity. Here, the initial equation contains a distribution of \(-1\).
By dividing both sides of the equation by \(-1\), we transform it into a simpler form: \( y + 3 = -10 \). This action eliminates the multiplication and helps us clearly see the relationship between \( y \) and the numbers. Simplifying an equation often involves reviewing and performing operations such as:

• Removing brackets by distributing.
• Combining like terms if present.
• Canceling out unnecessary coefficients or factors.

Remember, a simplified equation is easier to work with and more transparent, which is why it's a key step in solving equations.

Basic algebra provides the foundation for solving equations like \(-1(y + 3) = 10\). It involves understanding and applying simple principles and operations to find unknown values. To solve such equations, you generally follow a sequence:
1. **Understand the logical flow:** An equation states that two expressions are equal. 2. **Perform operations on both sides:** Any operation applied to one side must be applied to the other to maintain balance. 3. **Use inverse operations:** These help cancel out numbers or coefficients attached to the variable.In this specific example, we started by reversing the distribution of \(-1\). Then, continued by subtracting terms to isolate \( y \). Lastly, simplifying what was left gave us the solution. Basic algebra often involves just a few straightforward steps, but mastering these can turn complex mathematical situations into manageable ones.