Solve Linear Equation: 12y+4y+5-3=2y for Variable y

Linear Equations with Combining Terms

12y+4y+5−3=2y 12y+4y+5-3=2y

y=? 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
00:14 Isolate the unknown Y
00:29 Reduce what we can
00:35 Isolate the unknown Y
00:46 Factor 14 into terms 7 and 2
00:55 Reduce what we can
01:00 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12y+4y+5−3=2y 12y+4y+5-3=2y

y=? y=\text{?}

2

Step-by-step solution

To solve the equation 12y+4y+5−3=2y12y + 4y + 5 - 3 = 2y, we'll follow these steps:

  • **Step 1**: Simplify the left side of the equation by combining like terms: 12y+4y=16y12y + 4y = 16y.
  • **Step 2**: Replace that in the equation: 16y+5−3=2y16y + 5 - 3 = 2y. Simplify further to 16y+2=2y16y + 2 = 2y.
  • **Step 3**: Isolate yy by getting all the terms involving yy on one side. Subtract 2y2y from both sides, yielding: 16y−2y=−216y - 2y = -2.
  • **Step 4**: This simplifies to 14y=−214y = -2.
  • **Step 5**: Divide each side by 14 to solve for yy: y=−214y = \frac{-2}{14}.
  • **Step 6**: Simplify the fraction: y=−17y = -\frac{1}{7}.

Therefore, the solution to the problem is y=−17 y = -\frac{1}{7} .

3

Final Answer

−17 -\frac{1}{7}

Key Points to Remember

Essential concepts to master this topic
  • Combine Like Terms: Group all y terms together first
  • Technique: 12y + 4y = 16y, then 16y - 2y = 14y
  • Check: Substitute y=−17 y = -\frac{1}{7} : 16(-1/7) + 2 = 2(-1/7) ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to combine like terms on the same side
    Don't leave 12y + 4y uncombined = makes the equation much harder to solve! Students often jump straight to moving terms across the equals sign without simplifying first. Always combine all like terms on each side before isolating the variable.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why do I need to combine 12y + 4y first?

+

Combining like terms simplifies your equation and makes it easier to solve! Instead of dealing with multiple y terms, you get one clean term: 16y 16y .

What's the difference between 5 - 3 and -5 + 3?

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Both equal 2, but order matters for clarity! When you see 5 - 3, just calculate left to right. The key is being consistent with your arithmetic.

How do I know which terms to move to which side?

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Move all variable terms to one side and all number terms to the other. It doesn't matter which side you choose - just be consistent!

Why is my answer negative?

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Negative answers are completely normal! In this problem, we get y=−17 y = -\frac{1}{7} because we end up with -2 ÷ 14.

How do I simplify -2/14?

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Find the greatest common factor of 2 and 14, which is 2. Divide both numerator and denominator: −214=−17 \frac{-2}{14} = \frac{-1}{7} .

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