91Ó°ÊÓ

To solve any linear equation, our first aim is to isolate the variable term on one side of the equation. This means we need to have only the variable and its coefficients on one side, and all constants on the other side. For example, in the equation \(5x + 4 = 3x - 4\) , we need to move all terms involving \(x\) to one side and constants to the other. We do this by performing operations such as addition or subtraction on both sides of the equation.

For our specific example, we start by subtracting \(3x\) from both sides:
[5x + 4 - 3x = 3x - 4 - 3x]
This simplifies to:
[2x + 4 = -4]. This means all variable terms are now isolated on one side while all constants are on the other side.

Remember, performing the same operation on both sides of the equation keeps it balanced!

Combining like terms is crucial in simplifying any equation to make it easier to solve. Like terms are terms in the equation that have the same variable raised to the same power. For instance, in our equation \(5x + 4 - 3x = -4\), the terms \(5x\) and \(- 3x\) are like terms.

To combine them, we subtract \(3x\) from \(5x\):
[5x - 3x = 2x].
This gives us:
[2x + 4 = -4].
By combining the like terms, we reduce the complexity of the equation, making it much simpler to isolate the variable and ultimately solve for it.

Remember to perform operations carefully to avoid mistakes!

Once we have isolated the variable terms and combined like terms, the next step is to solve for the variable. In our equation \(2x + 4 = -4\), we first need to further isolate \(x\) by subtracting 4 from both sides:
[2x + 4 - 4 = -4 - 4].
This simplifies to:
[2x = -8].

The final step is to solve for \(x\). We do this by dividing both sides by the coefficient of \(x\), which is 2 in this case:
\[ \frac{2x}{2} = \frac{-8}{2} \ x = -4. \].

This means the value of \(x\) is \(-4\).

Always perform a quick check by substituting the value back into the original equation to ensure the solution is correct!