Evaluate the Expression: 8(x-7)+4(6-2y) with x=8 and y=5

Q: Do I substitute the values first or simplify the expression first?

Always substitute first! Replace x = 8 and y = 5 into the original expression, then simplify step by step. Don't try to expand algebraically first.

Q: Why did I get a positive answer when the correct answer is negative?

Check your work with negative numbers! In this problem, $ 6 - 2 \times 5 = 6 - 10 = -4 $, and $ 4 \times (-4) = -16 $. Missing the negative sign is very common.

Q: What's the most important thing to remember with parentheses?

Work inside the parentheses first! Calculate $ (8-7) $ and $ (6-2 \times 5) $ before multiplying by 8 and 4. This follows the order of operations.

Q: How can I check if my final answer is correct?

Substitute your values again and recalculate! Work through $ 8(8-7) + 4(6-2 \times 5) $ step by step. You should get -8 if done correctly.

Q: What if I forget which variable has which value?

Write down x = 8, y = 5 at the top of your work! Keep referring back to this as you substitute. It prevents mixing up the values.

Substitution and Simplification with Variable Values

What will be the result of this algebraic expression:

$8(x-7)+4(6-2y)$

if we place

$x=8,y=5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

00:03 Substitute appropriate values according to the given data and solve

00:19 Always solve parentheses first

00:29 Always solve multiplication and division before addition and subtraction

00:42 Positive times negative always equals negative

00:48 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What will be the result of this algebraic expression:

$8(x-7)+4(6-2y)$

if we place

$x=8,y=5$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Substitute the given values into the expression.
Step 2: Simplify the expression step-by-step.
Step 3: Evaluate and find the final result.

Now, let's work through each step:

Step 1: Substitute $x = 8$ and $y = 5$ into the expression:
$8(x-7) + 4(6-2y) \rightarrow 8(8-7) + 4(6-2 \times 5)$ .

Step 2: Simplify the expression:
- First, evaluate $8(8-7)$ . Since $(8-7) = 1$ , we have:
$8 \times 1 = 8$ .

- Next, evaluate $4(6-2 \times 5)$ . Compute $2 \times 5 = 10$ , so $6 - 10 = -4$ .
Therefore, $4 \times (-4) = -16$ .

Step 3: Combine the terms:
$8 + (-16) = 8 - 16 = -8$ .

Therefore, the solution to the problem is $-8$ .

Final Answer

$-8$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Always follow PEMDAS when substituting values into expressions
Substitution: Replace variables first: 8(8-7) + 4(6-2×5) becomes 8(1) + 4(-4)
Check: Verify calculations step-by-step: 8 + (-16) = -8 ✓

Common Mistakes

Avoid these frequent errors

Substituting values incorrectly into expressions
Don't substitute x=8 and y=5 randomly throughout the expression = wrong calculations! Students often replace variables without following proper order or miss negative signs. Always substitute carefully and work inside parentheses first using PEMDAS.

Practice Quiz

Test your knowledge with interactive questions

Solve the algebraic expression $$ 5x-6 $$ given that $$ x=0 $$ .

FAQ

Everything you need to know about this question

Do I substitute the values first or simplify the expression first?

Always substitute first! Replace x = 8 and y = 5 into the original expression, then simplify step by step. Don't try to expand algebraically first.

Why did I get a positive answer when the correct answer is negative?

Check your work with negative numbers! In this problem, $6 - 2 \times 5 = 6 - 10 = -4$ , and $4 \times (-4) = -16$ . Missing the negative sign is very common.

What's the most important thing to remember with parentheses?

Work inside the parentheses first! Calculate $(8-7)$ and $(6-2 \times 5)$ before multiplying by 8 and 4. This follows the order of operations.

How can I check if my final answer is correct?

Substitute your values again and recalculate! Work through $8(8-7) + 4(6-2 \times 5)$ step by step. You should get -8 if done correctly.

What if I forget which variable has which value?

Write down x = 8, y = 5 at the top of your work! Keep referring back to this as you substitute. It prevents mixing up the values.

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