Solve the Linear Equation: 4 = 3y Step-by-Step

Linear Equations with Mixed Number Solutions

4=3y 4=3y

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Step-by-step video solution

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00:00 Solve
00:03 Isolate the unknown Y
00:06 This is the solution to the question

Step-by-step written solution

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1

Understand the problem

4=3y 4=3y

2

Step-by-step solution

The goal is to solve the equation 4=3y 4 = 3y to find the value of y y . To do this, we can follow these steps:

  • Step 1: Divide both sides of the equation by 3 to isolate y y .
  • Step 2: Simplify the result to solve for y y .

Now, let's work through the solution:

Step 1: We start with the equation:

4=3y 4 = 3y

To solve for y y , divide both sides by 3:

y=43 y = \frac{4}{3}

Step 2: Simplify the fraction:

y=43=113 y = \frac{4}{3} = 1 \frac{1}{3}

Therefore, the solution to the equation is y=113 y = 1 \frac{1}{3} .

This corresponds to choice y=113 y = 1\frac{1}{3} in the provided multiple-choice answers.

3

Final Answer

y=113 y=1\frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Divide both sides by the coefficient to isolate the variable
  • Technique: Divide 4 ÷ 3 to get 43 \frac{4}{3} or 113 1\frac{1}{3}
  • Check: Substitute back: 3×113=3×43=4 3 \times 1\frac{1}{3} = 3 \times \frac{4}{3} = 4

Common Mistakes

Avoid these frequent errors
  • Dividing the variable instead of its coefficient
    Don't divide y by 3 to get y3 \frac{y}{3} = wrong variable manipulation! This keeps the coefficient attached and doesn't isolate y. Always divide both sides by the entire coefficient (3) to get y=43 y = \frac{4}{3} .

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( 5x=25 \)

FAQ

Everything you need to know about this question

Why do I need to divide both sides by 3?

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To isolate the variable y, you need to undo the multiplication by 3. Since 3y 3y means 3 times y, you divide both sides by 3 to cancel it out.

How do I convert 43 \frac{4}{3} to a mixed number?

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Divide 4 by 3: 4 ÷ 3 = 1 remainder 1. So 43=113 \frac{4}{3} = 1\frac{1}{3} . The whole number is the quotient, and the remainder becomes the new numerator.

Can I leave my answer as an improper fraction?

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Yes! 43 \frac{4}{3} is mathematically correct. However, mixed numbers like 113 1\frac{1}{3} are often preferred because they're easier to visualize and understand.

What if I multiply both sides by 3 instead?

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That would give you 12=9y 12 = 9y , making the problem more complicated! When the variable has a coefficient, always divide by that coefficient to isolate it quickly.

How can I check if 113 1\frac{1}{3} is correct?

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Substitute back: 3×113=3×43=123=4 3 \times 1\frac{1}{3} = 3 \times \frac{4}{3} = \frac{12}{3} = 4 . Since this equals the original right side, your answer is correct!

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