91Ó°ÊÓ

In algebra, when you're given a specific value for a variable, the first step is usually to substitute that value into the equation. This means replacing the variable in the equation with the given number. For instance, in the exercise above, we substitute the value of \( x = -8 \) into every appearance of \( x \) in the equation \(-5 - 2(x-5) = -(x+3)\).
This initial step is crucial because it transforms the equation from one that's based on a variable to one that's now a numerical expression. Think of it like filling in the blanks: you're putting in the specific number where a letter was. This makes it easier to work with and to understand the subsequent steps of solving the equation.

After substituting the values into the equation, the next essential step is simplifying the expressions on both sides of the equation. Simplifying means performing the arithmetic operations such as addition, subtraction, multiplication, or division as needed. It helps us to condense and reduce the equation to simpler terms, making it easier to compare later.

• For the left side, substitute \( x = -8 \) which gives you \(-5 - 2(-13) = 21\) after simplification.
• On the right side, the substitution results in \(-(-(8+3)) = 5\).

Simplifying can involve several steps, including: removing parentheses, combining like terms, and performing arithmetic operations. It is one of the fundamental skills in algebra and becomes a lot easier with practice.

Once you have simplified both sides of the equation, the final step is to compare these expressions to see if they are equal. Comparing tells us whether the value initially substituted satisfies the equation.For the exercise, after simplifying, the left-hand side becomes \(21\), and the right-hand side becomes \(5\). Since \(21 eq 5\), we can conclude that the given value \( x = -8 \) does not solve the equation, as the expressions are not equivalent.
Comparing expressions is the pivotal verification step. It answers the "Yes or No" question of whether the substituted value results in a true statement when plugged back into the equation. If the simplified expressions are equal, then the substituted value is a solution. If not, another value must be tried or the problem must be re-evaluated.