Solve the Fraction Equation: Find X in 2/3x - 4/6 = 1/3

Linear Equations with Fractional Simplification

Solve for X:
23x−46=13 \frac{2}{3}x-\frac{4}{6}=\frac{1}{3}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve the problem together.
00:08 First, we need to isolate the unknown X.
00:13 Arrange the equation so that X is on one side.
00:27 Next, simplify the equation by reducing common terms.
00:32 Factor 4 into 2 and 2, and 6 into 2 and 3.
00:44 Great! Reduce the terms we can.
00:49 Now, let's group like terms together.
00:58 Finally, isolate X and calculate its value.
01:15 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:
23x−46=13 \frac{2}{3}x-\frac{4}{6}=\frac{1}{3}

2

Step-by-step solution

Let's solve the equation 23x−46=13 \frac{2}{3}x - \frac{4}{6} = \frac{1}{3} .

Step 1: Simplify the fractions.

  • The term 46\frac{4}{6} is equivalent to 23\frac{2}{3} after simplification.

Now, the equation can be rewritten as:

23x−23=13\frac{2}{3}x - \frac{2}{3} = \frac{1}{3}

Step 2: Add 23\frac{2}{3} to both sides to isolate the term with x x .

23x=13+23\frac{2}{3}x = \frac{1}{3} + \frac{2}{3}

Simplify the right side:

23x=33\frac{2}{3}x = \frac{3}{3}

33=1\frac{3}{3} = 1

So the equation becomes:

23x=1\frac{2}{3}x = 1

Step 3: Solve for x x by multiplying both sides by the reciprocal of 23\frac{2}{3}.

Multiply both sides by 32\frac{3}{2}:

x=1×32x = 1 \times \frac{3}{2}

Thus, the solution is:

x=32x = \frac{3}{2}

The solution to the problem is x=32 x = \frac{3}{2} .

3

Final Answer

32 \frac{3}{2}

Key Points to Remember

Essential concepts to master this topic
  • Simplification: Always reduce fractions to lowest terms before solving
  • Technique: 46=23 \frac{4}{6} = \frac{2}{3} makes the equation easier to handle
  • Check: Substitute x=32 x = \frac{3}{2} back: 23⋅32−23=13 \frac{2}{3} \cdot \frac{3}{2} - \frac{2}{3} = \frac{1}{3} ✓

Common Mistakes

Avoid these frequent errors
  • Not simplifying fractions before solving
    Don't leave 46 \frac{4}{6} unsimplified = messy calculations with larger numbers! This makes the problem harder and increases chances of arithmetic errors. Always simplify fractions like 46=23 \frac{4}{6} = \frac{2}{3} first to work with smaller, cleaner numbers.

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 should I simplify 46 \frac{4}{6} to 23 \frac{2}{3} first?

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Simplifying makes the math much easier! Working with 23 \frac{2}{3} instead of 46 \frac{4}{6} gives you smaller numbers and reduces calculation errors.

What if I forget to simplify and solve with 46 \frac{4}{6} ?

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You'll still get the right answer, but it will be much harder work! You'll deal with larger fractions like 64 \frac{6}{4} instead of the simpler 32 \frac{3}{2} .

How do I add fractions with the same denominator like 13+23 \frac{1}{3} + \frac{2}{3} ?

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When denominators are the same, just add the numerators: 13+23=1+23=33=1 \frac{1}{3} + \frac{2}{3} = \frac{1+2}{3} = \frac{3}{3} = 1 . Keep the denominator the same!

Why do I multiply by 32 \frac{3}{2} to solve 23x=1 \frac{2}{3}x = 1 ?

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Because 32 \frac{3}{2} is the reciprocal of 23 \frac{2}{3} ! When you multiply a fraction by its reciprocal, you get 1, which isolates x.

How can I check if x=32 x = \frac{3}{2} is correct?

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Substitute back into the original equation: 23⋅32−46=1−23=13 \frac{2}{3} \cdot \frac{3}{2} - \frac{4}{6} = 1 - \frac{2}{3} = \frac{1}{3} ✓. If both sides equal 13 \frac{1}{3} , you're right!

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