Solve for X in the Equation: 3(x-2)=4 | Linear Equation Practice

Linear Equations with Distributive Property

Solve for X:

3(x−2)=4 3(x-2)=4

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 Make sure to open parentheses properly, multiply by each factor
00:20 Positive times negative is always negative
00:26 Arrange the equation so that one side has only the unknown X
00:37 Group terms
00:42 Isolate X
00:51 Simplify what we can
00:56 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:

3(x−2)=4 3(x-2)=4

2

Step-by-step solution

To solve the equation 3(x−2)=4 3(x-2) = 4 , we follow these detailed steps:

  • Step 1: Apply the distributive property to the left side of the equation. This means multiplying 3 by each term within the parentheses.
  • Step 2: Expand 3(x−2) 3(x-2) to get 3x−6 3x - 6 .
  • Step 3: The equation is now 3x−6=4 3x - 6 = 4 .
  • Step 4: To isolate the term containing x x , add 6 to both sides of the equation. This yields 3x−6+6=4+6 3x - 6 + 6 = 4 + 6 , simplifying to 3x=10 3x = 10 .
  • Step 5: Divide both sides of the equation by 3 to solve for x x . So, x=103 x = \frac{10}{3} .

Therefore, the solution to the problem is x=103 x = \frac{10}{3} .

3

Final Answer

103 \frac{10}{3}

Key Points to Remember

Essential concepts to master this topic
  • Distributive Property: Multiply outside number by each term inside parentheses
  • Technique: 3(x-2) becomes 3x - 6, then solve 3x - 6 = 4
  • Check: Substitute x = 10/3: 3(10/3 - 2) = 3(4/3) = 4 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute to all terms in parentheses
    Don't multiply 3 × x only and leave -2 unchanged = 3x - 2 = 4! This skips the distributive property and gives x = 2 instead of 10/3. Always multiply the outside number by every term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Solve for \( b \):

\( 8-b=6 \)

FAQ

Everything you need to know about this question

Why can't I just divide both sides by 3 first?

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You can't divide by 3 first because the 3 is multiplying the entire expression (x-2), not just x. You must use the distributive property to expand 3(x-2) before isolating x.

What if I get confused with the negative sign?

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Remember that 3(x-2) means 3 times x plus 3 times (-2). So you get 3x + 3(-2) = 3x - 6. The negative stays with the 2!

How do I handle fractions in my final answer?

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The fraction 103 \frac{10}{3} is already in lowest terms since 10 and 3 share no common factors. You can leave it as an improper fraction or convert to mixed number: 313 3\frac{1}{3} .

Can I check my answer a different way?

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Yes! Besides substituting back, you can work backwards: if x = 10/3, then x - 2 = 10/3 - 6/3 = 4/3. Then 3 × 4/3 = 4. Both methods should give you 4!

What if I made an arithmetic mistake?

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Common spots for errors: when subtracting 2 from 10/3, remember to convert 2 to sixths: 10/3 - 6/3 = 4/3. Always use common denominators when adding or subtracting fractions.

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