Solve the Fraction Equation: Finding X in 1/5x = 12

Linear Equations with Fractional Coefficients

Solve for X:

15x=12 \frac{1}{5}x=12

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to isolate the unknown X
00:09 To eliminate the fraction, multiply by the denominator
00:15 Let's arrange the equation so that one side has only the unknown X
00:27 Simplify what we can
00:35 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

Solve for X:

15x=12 \frac{1}{5}x=12

2

Step-by-step solution

To solve this problem, we will follow the steps outlined below:

  • Step 1: Recognize that 15x=12 \frac{1}{5}x = 12 gives us x x multiplied by 15 \frac{1}{5} .
  • Step 2: Multiply both sides of the equation by 5 to eliminate the fraction.
  • Step 3: Simplify the resulting equation to solve for x x .

Let's proceed step-by-step:

Step 1: We have the equation 15x=12 \frac{1}{5}x = 12 .

Step 2: To isolate x x , multiply both sides of the equation by 5:

5×15x=5×12 5 \times \frac{1}{5}x = 5 \times 12

Step 3: Simplify both sides:

  • The left side simplifies to x x because 5×15=1 5 \times \frac{1}{5} = 1 , so x x is left alone.
  • The right side becomes 60 60 , since 5×12=60 5 \times 12 = 60 .

Therefore, the value of x x is 60 60 .

Therefore, the solution to the problem is x=60 x = 60 .

3

Final Answer

60 60

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply both sides by the denominator to eliminate fractions
  • Technique: Multiply 15x=12 \frac{1}{5}x = 12 by 5 to get x = 60
  • Check: Substitute back: 15(60)=12 \frac{1}{5}(60) = 12

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting the denominator instead of multiplying
    Don't add 5 to both sides to get x=17 x = 17 ! This doesn't eliminate the fraction at all. Always multiply both sides by the denominator to isolate the variable.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( x - 3 + 5 = 8 - 2 \)

FAQ

Everything you need to know about this question

Why do I multiply both sides by 5?

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When you have 15x \frac{1}{5}x , you need to cancel out the fraction. Multiplying by 5 makes 5×15=1 5 \times \frac{1}{5} = 1 , leaving just x on the left side!

What if the fraction was 2/5 instead of 1/5?

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You'd still multiply both sides by 5! For 25x=12 \frac{2}{5}x = 12 , you get 2x=60 2x = 60 , then divide both sides by 2 to get x = 30.

Can I flip the fraction instead of multiplying?

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No! Flipping only works when the entire side is a fraction. Since we have 15x \frac{1}{5}x (not just a fraction), we must multiply by the denominator.

How do I check if x = 60 is correct?

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Substitute 60 back into the original equation: 15(60)=605=12 \frac{1}{5}(60) = \frac{60}{5} = 12 . Since this equals 12, your answer is correct!

What if I get a decimal answer instead?

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That's okay! Some fraction equations give decimal answers. Just make sure to check your work by substituting back into the original equation.

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