4y/2x evaluate the expression when x=4 and y= -6

4y/2x evaluate the expression when x=4 and y= -6

The correct answer and explanation is:

We are given the algebraic expression: 4y2x\frac{4y}{2x}

and asked to evaluate it when x=4x = 4 and y=−6y = -6.

Step-by-step solution:

1. Substitute the values of xx and yy into the expression:

4(−6)2(4)\frac{4(-6)}{2(4)}

2. Multiply the numerator:

4×(−6)=−244 \times (-6) = -24

3. Multiply the denominator:

2×4=82 \times 4 = 8

4. Divide:

−248=−3\frac{-24}{8} = -3

✅ Final Answer:

−3\boxed{-3}

💡 Explanation (300 words):

This problem involves evaluating an algebraic expression by replacing variables with specific values. The expression is: 4y2x\frac{4y}{2x}

This fraction has variables in both the numerator and the denominator. To evaluate it, we first substitute the values of the variables. In this case, we’re told:

• x=4x = 4
• y=−6y = -6

So we plug these values into the expression: 4(−6)2(4)\frac{4(-6)}{2(4)}

Now we perform the multiplication in both the numerator and denominator. In the numerator, 4×(−6)=−244 \times (-6) = -24. In the denominator, 2×4=82 \times 4 = 8.

Now we divide: −248=−3\frac{-24}{8} = -3

This tells us that when x=4x = 4 and y=−6y = -6, the entire expression simplifies to −3-3.

This type of evaluation is very common in algebra. It’s important to follow the order of operations (PEMDAS/BODMAS) and handle signs (positive/negative) carefully. Also, be cautious to substitute correctly — one small mistake in multiplication or sign handling can lead to a wrong answer.

Understanding how to substitute and simplify algebraic expressions is a key algebra skill that prepares you for solving equations, graphing, and real-world applications like physics or economics problems.