Solution: Step 1: Utilize the distributive property to multiply frac12 by each term inside the parentheses: frac12 cdot 4x + frac12 cdot (-5). Step 2: Identify and eliminate the common factor of 2. Step 2.1: Extract the factor of 2 from 4x: frac12 cdot (2 cdot 2x) + frac12 cdot (-5). Step 2.2: Simplify by removing the common factor: frac1cancel2 cdot (cancel2 cdot 2x) + frac12 cdot (-5). Step 2.3: Present the simplified expression: 2x + frac12 cdot (-5). Step 3: Merge the terms frac12 and -5: 2x + frac-52. Step 4: Adjust the negative sign to precede the fraction: 2x - frac52. Knowledge Notes: The problem-solving process involves simplifying an algebraic expression that includes a fraction and a variable. The key steps in this process include: 1. Distributive Property: This property states that a(b + c) = ab + ac. It allows us to multiply a single term by each term inside a set of parentheses. 2. Simplifying Fractions: When a common factor exists between the numerator and denominator, it can be canceled out to simplify the expression. 3. Combining Like Terms: This involves adding or subtracting terms that have the same variable raised to the same power. 4. Negative Fractions: When a fraction has a negative sign, it can be placed either in the numerator, denominator, or in front of the entire fraction without changing the value of the expression. In the given problem, we apply these principles to simplify the expression 1/2 cdot (4x - 5), ultimately arriving at 2x - 5/2.

Simplify 1/2*(4x-5)

Brief Explanation of the Question:

The question asks to perform a simplification on a mathematical expression. Specifically, it involves a binomial expression (4x - 5) being multiplied by a fraction, which is one-half (1/2). To simplify the given problem, one would need to apply the distributive property, multiplying each term inside the parentheses by the fraction that is outside, in this case, 1/2. This operation would lead to a simplified expression, where each term in the binomial is halved. The expected output is to provide this simplified form without actually carrying out the calculation step by step.

$\frac{1}{2} \cdot \left(\right. 4 x - 5 \left.\right)$

Answer

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Solution:

Step 1:

Utilize the distributive property to multiply $\frac{1}{2}$ by each term inside the parentheses: $\frac{1}{2} \cdot 4x + \frac{1}{2} \cdot (-5)$.

Step 2:

Identify and eliminate the common factor of 2.

Step 2.1:

Extract the factor of 2 from $4x$: $\frac{1}{2} \cdot (2 \cdot 2x) + \frac{1}{2} \cdot (-5)$.

Step 2.2:

Simplify by removing the common factor: $\frac{1}{\cancel{2}} \cdot (\cancel{2} \cdot 2x) + \frac{1}{2} \cdot (-5)$.

Step 2.3:

Present the simplified expression: $2x + \frac{1}{2} \cdot (-5)$.

Step 3:

Merge the terms $\frac{1}{2}$ and $-5$: $2x + \frac{-5}{2}$.

Step 4:

Adjust the negative sign to precede the fraction: $2x - \frac{5}{2}$.

Knowledge Notes:

The problem-solving process involves simplifying an algebraic expression that includes a fraction and a variable. The key steps in this process include:

Distributive Property: This property states that $a(b + c) = ab + ac$. It allows us to multiply a single term by each term inside a set of parentheses.
Simplifying Fractions: When a common factor exists between the numerator and denominator, it can be canceled out to simplify the expression.
Combining Like Terms: This involves adding or subtracting terms that have the same variable raised to the same power.
Negative Fractions: When a fraction has a negative sign, it can be placed either in the numerator, denominator, or in front of the entire fraction without changing the value of the expression.

In the given problem, we apply these principles to simplify the expression $1/2 \cdot (4x - 5)$, ultimately arriving at $2x - 5/2$.