Solve the Expression: 8(x-7)+4(6-2y) with x=7.1 and y=5/8

Q: Should I convert the fraction to a decimal first?

Yes! Converting $ \frac{5}{8} = 0.625 $ makes the arithmetic much easier. You can also keep it as a fraction, but decimals are usually simpler for substitution problems.

Q: Why did we get 0.8 for the first part?

When $ x = 7.1 $, we have $ x - 7 = 7.1 - 7 = 0.1 $. Then $ 8 \times 0.1 = 0.8 $. The key is doing the subtraction inside parentheses first!

Q: Can I work with the fraction form throughout?

Absolutely! $ 2y = 2 \times \frac{5}{8} = \frac{10}{8} = \frac{5}{4} $, then $ 6 - \frac{5}{4} = \frac{24}{4} - \frac{5}{4} = \frac{19}{4} $, and finally $ 4 \times \frac{19}{4} = 19 $.

Q: What if I made an error in my calculations?

Double-check each step! Most errors happen in fraction-to-decimal conversion or order of operations. Work slowly and verify: $ \frac{5}{8} = 5 \div 8 = 0.625 $.

Q: Do I need to show every single step?

Yes! For substitution problems, show: (1) Original expression, (2) Values substituted, (3) Parentheses calculated, and (4) Final arithmetic. This prevents errors!

Algebraic Substitution with Mixed Number Types

What will be the result of this algebraic expression:

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

if we place

$x=7.1,y=\frac{5}{8}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Substitute and solve

00:03 Let's substitute appropriate values according to the given data and solve

00:22 Always solve parentheses first

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

00:33 Negative times positive always equals negative

00:44 Continue solving according to the correct order of operations

01:03 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

$x=7.1,y=\frac{5}{8}$

Step-by-step solution

To solve the problem, we need to substitute the given values into the expression and simplify:

Step 1: Substitute $x = 7.1$ into the expression $8(x-7)$ .
This gives us $8(7.1-7) = 8(0.1) = 0.8$ .
Step 2: Substitute $y = \frac{5}{8}$ into the expression $4(6-2y)$ .
First, calculate $2y = 2 \times \frac{5}{8} = \frac{10}{8} = 1.25$ .
Then, $6 - 1.25 = 4.75$ .
Finally, $4(4.75) = 19$ .
Step 3: Add the results from Step 1 and Step 2.
That is $0.8 + 19 = 19.8$ .

Therefore, the result of the expression $8(x-7) + 4(6-2y)$ with $x = 7.1$ and $y = \frac{5}{8}$ is $\mathbf{19.8}$ .

Final Answer

$19.8$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: First substitute values, then work inside parentheses
Technique: Convert $\frac{5}{8}$ to 0.625 for easier calculations
Check: Verify 8(0.1) + 4(4.75) = 0.8 + 19 = 19.8 ✓

Common Mistakes

Avoid these frequent errors

Adding variables before substitution
Don't try to simplify 8(x-7) + 4(6-2y) algebraically first = complicated mess! This makes substitution much harder and leads to calculation errors. Always substitute the given values immediately into the original expression.

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

Should I convert the fraction to a decimal first?

Yes! Converting $\frac{5}{8} = 0.625$ makes the arithmetic much easier. You can also keep it as a fraction, but decimals are usually simpler for substitution problems.

Why did we get 0.8 for the first part?

When $x = 7.1$ , we have $x - 7 = 7.1 - 7 = 0.1$ . Then $8 \times 0.1 = 0.8$ . The key is doing the subtraction inside parentheses first!

Can I work with the fraction form throughout?

Absolutely! $2y = 2 \times \frac{5}{8} = \frac{10}{8} = \frac{5}{4}$ , then $6 - \frac{5}{4} = \frac{24}{4} - \frac{5}{4} = \frac{19}{4}$ , and finally $4 \times \frac{19}{4} = 19$ .

What if I made an error in my calculations?

Double-check each step! Most errors happen in fraction-to-decimal conversion or order of operations. Work slowly and verify: $\frac{5}{8} = 5 \div 8 = 0.625$ .

Do I need to show every single step?

Yes! For substitution problems, show: (1) Original expression, (2) Values substituted, (3) Parentheses calculated, and (4) Final arithmetic. This prevents errors!

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