Solve Linear Equation: 2x+4+28-3x=x Step by Step

Linear Equations with Like Term Combination

2x+4+283x=x 2x+4+28-3x=x

x=? x=?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Gather terms
00:10 Isolate the unknown X
00:25 Calculate the fraction
00:29 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

2x+4+283x=x 2x+4+28-3x=x

x=? x=?

2

Step-by-step solution

To solve this problem, we will simplify and solve the linear equation step-by-step:

1. Start with the given equation:
2x+4+283x=x 2x + 4 + 28 - 3x = x

2. Combine like terms on the left side:
(2x3x)+4+28=x (2x - 3x) + 4 + 28 = x

3. This simplifies to:
x+32=x -x + 32 = x

4. Move all terms involving x x to one side of the equation by adding x x to both sides:
32=2x 32 = 2x

5. Finally, divide both sides by 2 to solve for x x :
x=322 x = \frac{32}{2}

6. Simplify to get the solution:
x=16 x = 16

Therefore, the solution to the problem is x=16 \mathbf{x = 16} .

3

Final Answer

16

Key Points to Remember

Essential concepts to master this topic
  • Rule: Combine like terms first before moving variables to one side
  • Technique: Group coefficients: (2x - 3x) = -x and constants: 4 + 28 = 32
  • Check: Substitute x = 16: 2(16) + 4 + 28 - 3(16) = 16 ✓

Common Mistakes

Avoid these frequent errors
  • Moving variables before combining like terms
    Don't move 2x and -3x to opposite sides separately = creates messy fractions and confusion! This makes the problem much harder than needed. Always combine like terms on each side first, then move variables.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( 3x=18 \)

FAQ

Everything you need to know about this question

Why do I combine like terms before moving variables?

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Combining like terms simplifies the equation first, making it easier to solve! In this problem, 2x3x=x 2x - 3x = -x is much simpler than dealing with separate x terms.

What if I get a negative coefficient for x?

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That's normal! When you have x=something -x = \text{something} , just multiply both sides by -1 to make x positive. Don't panic about negative coefficients!

How do I know which terms are 'like terms'?

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Like terms have the same variable and power. Here, 2x 2x and 3x -3x are like terms, while 4 4 and 28 28 are constant like terms.

Can I add the constants 4 + 28 right away?

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Yes! Constants are always like terms, so you can combine them immediately: 4+28=32 4 + 28 = 32 . This makes the equation cleaner to work with.

What does it mean when I get 32 = 2x?

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This means you successfully isolated the variable term! Now just divide both sides by 2 to find x=16 x = 16 . You're almost done!

How can I double-check my arithmetic?

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Work step by step: 2(16)=32 2(16) = 32 , 3(16)=48 3(16) = 48 , so 32+4+2848=16 32 + 4 + 28 - 48 = 16 . Both sides equal 16!

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