Solution: Step 1: Break down the expression Step 1.1: Use the distributive property 5x - 3(x - 2) - x = 5x - 3 cdot x + 3 cdot 2 - x Step 1.2: Perform the multiplication 5x - 3x + 6 - x Step 2: Combine like terms Step 2.1: Combine 5x and -3x 2x + 6 - x Step 2.2: Combine 2x and -x x + 6 Knowledge Notes: The problem-solving process involves simplifying an algebraic expression. Here are the relevant knowledge points: 1. Distributive Property: This property states that a(b + c) = ab + ac. It is used to eliminate parentheses by distributing the multiplication over addition or subtraction within the parentheses. 2. Combining Like Terms: This refers to the process of adding or subtracting terms that have the same variable raised to the same power. For example, 5x and -3x are like terms and can be combined to 2x. 3. Simplification: This involves reducing an expression to its simplest form by performing all possible operations, including the distributive property and combining like terms. 4. Subtraction of Variables: When subtracting variables, you subtract their coefficients. For instance, 5x - x would result in 4x. 5. Multiplication of Integers: When multiplying integers, the sign of the result depends on the signs of the integers being multiplied. For example, multiplying a negative by a negative, as in -3 cdot -2, gives a positive result. In the given problem, the distributive property is first applied to expand the expression and eliminate the parentheses. Then, like terms are combined to simplify the expression to its simplest form.

Simplify 5x-3(x-2)-x

The given problem asks to perform algebraic simplification on a given mathematical expression. The expression has multiple terms involving the variable 'x' combined with arithmetic operations such as multiplication and subtraction. The task is to apply the distributive property to remove parentheses, combine like terms, and simplify the expression to its most reduced form.

$5 x - 3 \left(\right. x - 2 \left.\right) - x$

Answer

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Solution:

Step 1: Break down the expression

Step 1.1: Use the distributive property

$5x - 3(x - 2) - x = 5x - 3 \cdot x + 3 \cdot 2 - x$

Step 1.2: Perform the multiplication

$5x - 3x + 6 - x$

Step 2: Combine like terms

Step 2.1: Combine $5x$ and $-3x$

$2x + 6 - x$

Step 2.2: Combine $2x$ and $-x$

$x + 6$

Knowledge Notes:

The problem-solving process involves simplifying an algebraic expression. Here are the relevant knowledge points:

Distributive Property: This property states that $a(b + c) = ab + ac$. It is used to eliminate parentheses by distributing the multiplication over addition or subtraction within the parentheses.
Combining Like Terms: This refers to the process of adding or subtracting terms that have the same variable raised to the same power. For example, $5x$ and $-3x$ are like terms and can be combined to $2x$.
Simplification: This involves reducing an expression to its simplest form by performing all possible operations, including the distributive property and combining like terms.
Subtraction of Variables: When subtracting variables, you subtract their coefficients. For instance, $5x - x$ would result in $4x$.
Multiplication of Integers: When multiplying integers, the sign of the result depends on the signs of the integers being multiplied. For example, multiplying a negative by a negative, as in $-3 \cdot -2$, gives a positive result.

In the given problem, the distributive property is first applied to expand the expression and eliminate the parentheses. Then, like terms are combined to simplify the expression to its simplest form.