Calculate y in y=4(2-6x) Given x=2: Expression Evaluation

Q: Why do I substitute x=2 first instead of simplifying the expression?

You must substitute first because you're evaluating the expression for a specific value. Trying to simplify $ y=4(2-6x) $ without knowing x doesn't give you a number!

Q: What's the correct order of operations inside the parentheses?

Inside $ (2-6x) $, do multiplication first: $ 6×2 = 12 $, then subtraction: $ 2-12 = -10 $. Remember PEMDAS!

Q: Why is my answer negative when I started with positive numbers?

When $ x=2 $, you get $ 6×2 = 12 $, making $ 2-12 = -10 $. Then $ 4×(-10) = -40 $. Negative results are common in algebra!

Q: How can I double-check my arithmetic?

Work step by step: $ x=2 $ → $ 6×2=12 $ → $ 2-12=-10 $ → $ 4×(-10)=-40 $. Each step should make sense before moving on.

Q: What if I accidentally chose -32 or -24?

You likely made an order of operations error. -32 comes from doing $ 4×2-6×2×4 $ incorrectly. -24 comes from forgetting to multiply by 4. Always work inside parentheses first!

Expression Evaluation with Variable Substitution

Calculate y given that $x=2$ and $y=4(2-6x)$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find Y by using the given value for X.

00:12 First, substitute the value of X into the equation.

00:20 Remember, solve inside the parentheses first, then do any multiplication.

00:30 Now, substitute the result from the parentheses back into the equation.

00:39 Next, solve the multiplication.

00:43 And that's how we find the answer to this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate y given that $x=2$ and $y=4(2-6x)$ .

Step-by-step solution

To solve for $y$ , we will proceed with these steps:

Step 1: Substitute the given value $x = 2$ into the equation $y = 4(2 - 6x)$ .
Step 2: Simplify the expression inside the parentheses.
Step 3: Perform the arithmetic operations to find $y$ .

Now, let's work through the steps:

Step 1: Substitute $x = 2$ into the equation:
$y = 4(2 - 6 \times 2)$

Step 2: Simplify the expression within the parentheses:
$2 - 6 \times 2 = 2 - 12 = -10$

Step 3: Calculate the value of $y$ by multiplying by 4:
$y = 4 \times (-10) = -40$

Therefore, the value of $y$ is $-40$ .

This solution corresponds to the choice:

Choice 3: $-40$

Final Answer

$-40$

Key Points to Remember

Essential concepts to master this topic

Rule: Always substitute the given value first before simplifying
Technique: Follow order of operations: 6×2 = 12, then 2-12 = -10
Check: Substitute back: when x=2, y=4(2-6×2)=4(-10)=-40 ✓

Common Mistakes

Avoid these frequent errors

Multiplying 4 by 2 first instead of following order of operations
Don't multiply 4×2 first to get 8(2-6x) = wrong structure! This changes the expression and gives incorrect results like -80. Always substitute the variable value first, then follow order of operations within parentheses.

Practice Quiz

Test your knowledge with interactive questions

Find a y when $$ x=2 $$

$$ y=5x $$

FAQ

Everything you need to know about this question

Why do I substitute x=2 first instead of simplifying the expression?

You must substitute first because you're evaluating the expression for a specific value. Trying to simplify $y=4(2-6x)$ without knowing x doesn't give you a number!

What's the correct order of operations inside the parentheses?

Inside $(2-6x)$ , do multiplication first: $6×2 = 12$ , then subtraction: $2-12 = -10$ . Remember PEMDAS!

Why is my answer negative when I started with positive numbers?

When $x=2$ , you get $6×2 = 12$ , making $2-12 = -10$ . Then $4×(-10) = -40$ . Negative results are common in algebra!

How can I double-check my arithmetic?

Work step by step: $x=2$ → $6×2=12$ → $2-12=-10$ → $4×(-10)=-40$ . Each step should make sense before moving on.

What if I accidentally chose -32 or -24?

You likely made an order of operations error. -32 comes from doing $4×2-6×2×4$ incorrectly. -24 comes from forgetting to multiply by 4. Always work inside parentheses first!

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