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In algebra, distribution refers to the process of multiplying a single term by each term within parentheses. This is applied when you have an equation where components are grouped together in parentheses. For example, in the expression \( -5(x + 2) \), the distribution involves multiplying \( -5 \) by both \( x \) and \( 2 \). So, \( -5(x + 2) \) becomes \[ -5 \cdot x - 5 \cdot 2 = -5x - 10. \] Distribution is essential before combining like terms or isolating variables in an equation. This ensures that all terms are individually accounted for, simplifying the process of solving the equation.

Combining like terms is a crucial step in simplifying algebraic equations. 'Like terms' are terms that contain the same variables raised to the same power. For example, \( 11x \) and \( -5x \) are like terms because they both contain the variable \( x \). When you combine like terms, you add or subtract the coefficients. In our equation \([11x - 5x - 10 = 6x + 5]\), combining like terms simplifies the left side to: \[ 11x - 5x - 10 = 6x - 10. \] Then, both sides contain like terms that can sometimes be further simplified. This step reduces the equation to a simpler form and makes it easier to solve.

Isolating variables involves rearranging the equation so that the variable you're solving for is on one side of the equation, and all other terms are on the opposite side. This process typically includes adding, subtracting, multiplying, or dividing both sides of the equation to get the variable by itself. In the given equation, \( 6x - 10 = 6x + 5 \), we can subtract \( 6x \) from both sides to isolate the constants, which gives \[ -10 = 5. \] This result is a contradiction, indicating that no value of \( x \) satisfies the equation. Isolating the variable helps in understanding the relationship between terms and identifying any inconsistencies or special cases, such as no solution or infinitely many solutions.