91Ó°ÊÓ

Isolating the variable means getting the variable alone on one side of the equation. This is usually the first step in solving a linear equation. In our example, the equation was \(2x + 10 = 24\). To isolate the variable term \(2x\), we need to remove the constant term (10) on the same side. We do this by performing the opposite operation. Since 10 is added to \(2x\), we subtract 10 from both sides:
\(2x + 10 - 10 = 24 - 10\)
which simplifies to:
\(2x = 14\).
By subtracting 10 from both sides, we have effectively isolated the term with the variable on one side of the equation.

Once you’ve found a solution, it’s essential to check it to ensure it is correct. This involves substituting the found value of the variable back into the original equation to see if both sides are equal. In our example, we found \(x = 7\).
We substitute \(x = 7\) back into the original equation \(2x + 10 = 24\):
\(2(7) + 10 = 24\)
Simplifying, we get:
\(14 + 10 = 24\)
which simplifies further to:
\(24 = 24\).
Since the left-hand side equals the right-hand side, the solution is verified to be correct. Checking solutions helps to catch any possible mistakes and confirms that the solution satisfies the original equation.

Basic algebra is a fundamental branch of mathematics that deals with variables and the rules for manipulating these variables in equations. Key operations in basic algebra include addition, subtraction, multiplication, and division. When solving linear equations, it's important to use these operations to isolate the variable and find its value.
Let's review the operations used in the provided example:
- We first subtracted 10 from both sides: \(2x + 10 - 10 = 24 - 10\), which simplifies to \(2x = 14\). This used the subtraction property of equality.
- Next, we divided both sides by 2: \(\frac{2x}{2} = \frac{14}{2}\), which simplifies to \(x = 7\). This used the division property of equality.
These properties help maintain the balance of the equation while simplifying it to find the variable’s value. Mastery of these operations is crucial for success in algebra.