91Ó°ÊÓ

The first step in solving the linear equation is to apply the distributive property. The distributive property lets us remove parentheses by distributing, or multiplying, a number across each term inside the parentheses. In this problem, we have 5(x - 4). This means we need to multiply 5 by both x and -4:

\[ 5(x - 4) = 5 \times x + 5 \times (-4) \]

Simplifying inside the parentheses, we get:

\[ 5x - 20 \]

Therefore, the equation transforms from:

\[ 5(x - 4) - 4x = 14 \]

to:

\[ 5x - 20 - 4x = 14 \]

Understanding how to use the distributive property correctly is crucial in breaking down and simplifying complex elements within an equation. This process helps in making sure we address each part of the equation accurately.

Once we have applied the distributive property, the next step is to combine like terms. Like terms are terms that involve the same variables raised to the same power. In the equation:

\[ 5x - 20 - 4x = 14 \]

we have two terms with x's: 5x and -4x. To combine them, we simply perform the operation:

\[ 5x - 4x = x \]

Thus, the equation simplifies to:

\[ x - 20 = 14 \]

Combining like terms helps in reducing the equation to a simpler form, making it easier for further operations. It's important to be thorough with this step to ensure that each like term is properly accounted for.

The final step in solving the linear equation is to isolate the variable. This means getting the variable, in this case x, by itself on one side of the equation. From the simplified equation:

\[ x - 20 = 14 \]

we need to get rid of -20. To do that, we perform the opposite operation, which is adding 20 to both sides:

\[ x - 20 + 20 = 14 + 20 \]

This simplifies to:

\[ x = 34 \]

Isolating the variable is an essential part of solving equations because it allows us to find the precise value of the unknown we are trying to solve for. Ensuring the variable is correctly isolated helps in verifying the solution's accuracy.