Solve for X: 3x + 2/3 = 4(x + 1/12) Linear Equation

Linear Equations with Mixed Fractions

3x+23=4(x+112) 3x+\frac{2}{3}=4(x+\frac{1}{12})

x=? x=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this problem step by step.
00:12 First, open the brackets, and multiply each term inside.
00:18 Next, our goal is to have X alone on one side.
00:24 Rearrange the equation, so X is isolated.
00:55 We can write twelve as four times three.
01:00 Let's simplify as much as possible.
01:12 Change negatives to positives where needed.
01:18 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3x+23=4(x+112) 3x+\frac{2}{3}=4(x+\frac{1}{12})

x=? x=\text{?}

2

Step-by-step solution

To solve the equation 3x+23=4(x+112)3x + \frac{2}{3} = 4 \left(x + \frac{1}{12}\right), we follow these steps:

Step 1: Distribute the 4 on the right-hand side.

4(x+112)=4x+4124(x + \frac{1}{12}) = 4x + \frac{4}{12} which simplifies to 4x+134x + \frac{1}{3}.

Step 2: Write down the modified equation.

The equation now reads: 3x+23=4x+133x + \frac{2}{3} = 4x + \frac{1}{3}.

Step 3: Rearrange the equation to collect like terms.

Subtract 3x3x from both sides: 3x+23−3x=4x+13−3x3x + \frac{2}{3} - 3x = 4x + \frac{1}{3} - 3x.

This simplifies to: 23=x+13\frac{2}{3} = x + \frac{1}{3}.

Step 4: Isolate xx.

Subtract 13\frac{1}{3} from both sides: 23−13=x\frac{2}{3} - \frac{1}{3} = x.

This simplifies to: x=13x = \frac{1}{3}.

Therefore, the solution to the equation is 13\boxed{\frac{1}{3}}.

3

Final Answer

13 \frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Apply 4 to each term inside parentheses
  • Technique: Simplify 412=13 \frac{4}{12} = \frac{1}{3} before combining like terms
  • Check: Substitute x=13 x = \frac{1}{3} : both sides equal 73 \frac{7}{3} ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute the 4 to both terms inside parentheses
    Don't multiply 4 only by x and ignore 112 \frac{1}{12} = missing 13 \frac{1}{3} term! This creates an incomplete equation that gives wrong answers like x=23 x = \frac{2}{3} . Always distribute the coefficient to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

\( 2(4-x)=8 \)

FAQ

Everything you need to know about this question

Why do I need to distribute the 4 first?

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The distributive property says you must multiply 4 by both terms inside the parentheses. Skipping this step leaves part of the equation unsolved!

How do I simplify 412 \frac{4}{12} ?

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Divide both numerator and denominator by their greatest common factor: 412=4÷412÷4=13 \frac{4}{12} = \frac{4 ÷ 4}{12 ÷ 4} = \frac{1}{3} . This makes the math much easier!

Can I move all x terms to one side first?

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You should distribute first, then move terms. Moving terms before distributing makes the problem more complicated and increases chances of errors.

What if I get confused with the fractions?

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Take it step by step! First distribute, then simplify any fractions you can, and finally combine like terms. Don't try to do everything at once.

How do I check my answer with fractions?

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Substitute x=13 x = \frac{1}{3} into the original equation. Calculate each side separately: Left side = 3(13)+23=73 3(\frac{1}{3}) + \frac{2}{3} = \frac{7}{3} , Right side = 4(13+112)=73 4(\frac{1}{3} + \frac{1}{12}) = \frac{7}{3} ✓

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