Solve Linear Equation: 7y + 10y + 5 = 2(y + 3)

Q: Why do I get a fraction as my answer instead of a whole number?

Many linear equations have fractional solutions like $ \frac{1}{15} $! This is completely normal. Not every equation results in nice whole number answers.

Q: How do I know when to combine like terms?

Like terms have the same variable with the same exponent. Here, 7y and 10y are like terms because both have y to the first power. Always combine them first to simplify!

Q: What's the best way to check my fractional answer?

Substitute $ y = \frac{1}{15} $ back into the original equation. Calculate each side separately: Left side = $ 17 \cdot \frac{1}{15} + 5 $, Right side = $ 2(\frac{1}{15} + 3) $. Both should equal $ \frac{92}{15} $.

Q: Can I work with decimals instead of fractions?

Yes! $ \frac{1}{15} \approx 0.0667 $, but keeping the exact fraction is usually better for checking your work since decimals can introduce rounding errors.

Q: What if I make an arithmetic mistake while combining terms?

Double-check: 7y + 10y = 17y (not 70y!). Write it out step by step and be careful with your addition. Small arithmetic errors lead to completely wrong final answers.

Linear Equations with Fractional Solutions

$7y+10y+5=2(y+3)$

$y=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Collect terms

00:08 Open parentheses properly, multiply by each term

00:16 We want to isolate the unknown Y

00:20 Arrange the equation so that one side has only the unknown Y

00:40 Isolate the unknown Y

00:47 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

$7y+10y+5=2(y+3)$

$y=\text{?}$

Step-by-step solution

To solve the equation $7y + 10y + 5 = 2(y + 3)$ , let's proceed as follows:

Step 1: Simplify the left side by combining like terms. The expression $7y + 10y$ combines to $17y$ , so we have $17y + 5 = 2(y + 3)$ .
Step 2: Expand the right side. Distribute the 2 across the parenthesis: $2(y + 3)$ becomes $2y + 6$ . The equation now reads $17y + 5 = 2y + 6$ .
Step 3: Isolate terms involving $y$ on one side. Subtract $2y$ from both sides: $17y - 2y + 5 = 6$ , which simplifies to $15y + 5 = 6$ .
Step 4: Isolate $15y$ by subtracting 5 from both sides: $15y = 6 - 5$ , which simplifies to $15y = 1$ .
Step 5: Solve for $y$ by dividing both sides by 15: $y = \frac{1}{15}$ .

Therefore, the solution to the problem is $\mathbf{y = \frac{1}{15}}$ .

Final Answer

$\frac{1}{15}$

Key Points to Remember

Essential concepts to master this topic

Combining Terms: Add like terms first: 7y + 10y = 17y
Distribution: Expand 2(y + 3) = 2y + 6 before solving
Verification: Check: 17(1/15) + 5 = 2(1/15 + 3) gives 6.133... = 6.133... ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute on the right side
Don't solve 17y + 5 = 2(y + 3) without expanding the right side first = you'll get stuck with parentheses! This makes it impossible to collect like terms properly. Always distribute multiplication over addition before moving terms around.

Practice Quiz

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Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I get a fraction as my answer instead of a whole number?

Many linear equations have fractional solutions like $\frac{1}{15}$ ! This is completely normal. Not every equation results in nice whole number answers.

How do I know when to combine like terms?

Like terms have the same variable with the same exponent. Here, 7y and 10y are like terms because both have y to the first power. Always combine them first to simplify!

What's the best way to check my fractional answer?

Substitute $y = \frac{1}{15}$ back into the original equation. Calculate each side separately: Left side = $17 \cdot \frac{1}{15} + 5$ , Right side = $2(\frac{1}{15} + 3)$ . Both should equal $\frac{92}{15}$ .

Can I work with decimals instead of fractions?

Yes! $\frac{1}{15} \approx 0.0667$ , but keeping the exact fraction is usually better for checking your work since decimals can introduce rounding errors.

What if I make an arithmetic mistake while combining terms?

Double-check: 7y + 10y = 17y (not 70y!). Write it out step by step and be careful with your addition. Small arithmetic errors lead to completely wrong final answers.

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Solve Linear Equation: 7y + 10y + 5 = 2(y + 3)

Linear Equations with Fractional Solutions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I get a fraction as my answer instead of a whole number?

How do I know when to combine like terms?

What's the best way to check my fractional answer?

Can I work with decimals instead of fractions?

What if I make an arithmetic mistake while combining terms?

🌟 Unlock Your Math Potential

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