Solve the Linear Equation: -7y = -27 Step by Step

Q: Do I have to convert my answer to a mixed number?

It depends on what the problem asks for! $ \frac{27}{7} $ and $ 3\frac{6}{7} $ are exactly the same value. Mixed numbers are often easier to visualize, but improper fractions work too.

Q: How do I convert 27/7 to a mixed number?

Divide the numerator by the denominator: 27 ÷ 7 = 3 remainder 6. The whole number is 3, and the remainder 6 becomes the new numerator: $ 3\frac{6}{7} $.

Q: What if I accidentally make the coefficient positive?

You'd get the wrong answer! If you solve $ 7y = -27 $ instead, you get $ y = -\frac{27}{7} $, which is negative. Always double-check the original equation's signs.

Q: Can I multiply both sides by -1/7 instead of dividing by -7?

Yes! Multiplying by $ -\frac{1}{7} $ is the same as dividing by -7. Both methods give you $ y = 3\frac{6}{7} $. Use whichever feels more comfortable!

Linear Equations with Negative Coefficients

$-7y=-27$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this math problem!

00:08 First, we want to focus on the unknown, Y.

00:12 Now, let's work on isolating the variable, Y.

00:15 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-7y=-27$

Step-by-step solution

To solve the equation $-7y = -27$ , we need to isolate the variable $y$ . We do this by performing the following steps:

Step 1: Divide both sides of the equation by $-7$ to solve for $y$ .

Performing this operation gives us:

-7y \div (-7) = -27 \div (-7)

Simplifying both sides, we have:

y = \frac{27}{7}

To express $\frac{27}{7}$ as a mixed number, we divide 27 by 7:

27 divided by 7 equals 3 with a remainder of 6. Hence, $\frac{27}{7} = 3\frac{6}{7}$ .

Therefore, the solution to the equation is $y = 3\frac{6}{7}$ .

Among the given choices, option 1 matches our result.

Therefore, the solution to the problem is $y = 3\frac{6}{7}$ .

Final Answer

$3\frac{6}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both sides by the coefficient to isolate the variable
Technique: Dividing negatives: $-27 \div (-7) = +\frac{27}{7}$
Check: Substitute back: $-7(3\frac{6}{7}) = -27$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting negative signs when dividing
Don't ignore the negative signs and just divide 27 by 7 = wrong positive answer! Negative divided by negative gives positive, but you must track both signs carefully. Always pay attention to negative signs and remember that $(-) \div (-) = (+)$ .

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why is the answer positive when both sides are negative?

Great observation! When you divide two negative numbers, the result is positive. Think of it as: $-27 \div (-7) = +\frac{27}{7}$ . The negative signs cancel out!

Do I have to convert my answer to a mixed number?

It depends on what the problem asks for! $\frac{27}{7}$ and $3\frac{6}{7}$ are exactly the same value. Mixed numbers are often easier to visualize, but improper fractions work too.

How do I convert 27/7 to a mixed number?

Divide the numerator by the denominator: 27 ÷ 7 = 3 remainder 6. The whole number is 3, and the remainder 6 becomes the new numerator: $3\frac{6}{7}$ .

What if I accidentally make the coefficient positive?

You'd get the wrong answer! If you solve $7y = -27$ instead, you get $y = -\frac{27}{7}$ , which is negative. Always double-check the original equation's signs.

Can I multiply both sides by -1/7 instead of dividing by -7?

Yes! Multiplying by $-\frac{1}{7}$ is the same as dividing by -7. Both methods give you $y = 3\frac{6}{7}$ . Use whichever feels more comfortable!

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