Solve for Y: 20y + 8×2 - 7 = 14 Linear Equation

Q: Why do I multiply 8×2 before subtracting 7?

The order of operations (PEMDAS) requires multiplication before addition or subtraction. So 8×2 = 16 first, then we have 20y + 16 - 7.

Q: How do I simplify the fraction 5/20?

Find the greatest common factor of 5 and 20, which is 5. Divide both numerator and denominator: $ \frac{5÷5}{20÷5} = \frac{1}{4} $

Q: Can I leave my answer as a decimal instead?

You could write $ \frac{1}{4} = 0.25 $, but fractions are often preferred in algebra because they're exact and easier to work with in further calculations.

Q: How do I check if y = 1/4 is correct?

Substitute back into the original equation: $ 20(\frac{1}{4}) + 8×2 - 7 = 5 + 16 - 7 = 14 $ ✓ It works!

Linear Equations with Fraction Solutions

Solve the equation and find Y:

$20\times y+8\times2-7=14$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve wherever possible according to the appendix and transfer the terms

00:06 Start with the multiplication operations

00:30 Continue with the subtraction operation

00:37 Subtract 9 from both sides in order to isolate the variable

01:05 Divide by 20 in order to determine Y

01:29 Reduce the numerator and denominator

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the equation and find Y:

$20\times y+8\times2-7=14$

Step-by-step solution

We begin by placing parentheses around the two multiplication exercises:

$(20\times y)+(8\times2)-7=14$

We then solve the exercises within the parentheses:

$20y+16-7=14$

We simplify:

$20y+9=14$

We move the sections:

$20y=14-9$

$20y=5$

We divide by 20:

$y=\frac{5}{20}$

$y=\frac{5}{5\times4}$

We simplify:

$y=\frac{1}{4}$

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Always multiply before adding or subtracting terms
Technique: Combine like terms: 16 - 7 = 9 before isolating variable
Check: Substitute $\frac{1}{4}$ : 20(1/4) + 16 - 7 = 14 ✓

Common Mistakes

Avoid these frequent errors

Skipping order of operations
Don't solve 20y + 8×2 - 7 = 14 by working left to right = wrong answer! This ignores multiplication priority and gives incorrect intermediate steps. Always multiply 8×2 first, then combine 16 - 7 = 9 before isolating y.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why do I multiply 8×2 before subtracting 7?

The order of operations (PEMDAS) requires multiplication before addition or subtraction. So 8×2 = 16 first, then we have 20y + 16 - 7.

How do I simplify the fraction 5/20?

Find the greatest common factor of 5 and 20, which is 5. Divide both numerator and denominator: $\frac{5÷5}{20÷5} = \frac{1}{4}$

Can I leave my answer as a decimal instead?

You could write $\frac{1}{4} = 0.25$ , but fractions are often preferred in algebra because they're exact and easier to work with in further calculations.

What if I get stuck combining 16 - 7?

Just do the arithmetic: 16 - 7 = 9. Then your equation becomes 20y + 9 = 14, and you subtract 9 from both sides to get 20y = 5.

How do I check if y = 1/4 is correct?

Substitute back into the original equation: $20(\frac{1}{4}) + 8×2 - 7 = 5 + 16 - 7 = 14$ ✓ It works!

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Solve for Y: 20y + 8×2 - 7 = 14 Linear Equation

Linear Equations with Fraction 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 multiply 8×2 before subtracting 7?

How do I simplify the fraction 5/20?

Can I leave my answer as a decimal instead?

What if I get stuck combining 16 - 7?

How do I check if y = 1/4 is correct?

🌟 Unlock Your Math Potential

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