Solve for X in the Linear Equation: 3x+5=2x+20

Linear Equations with Variable Isolation

Solve for X:

3x+5=2x+20 3x+5=2x+20

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

3x+5=2x+20 3x+5=2x+20

2

Step-by-step solution

To solve the equation 3x+5=2x+20 3x + 5 = 2x + 20 , we need to find the value of x x that satisfies this equation. Here are the detailed steps:

  • Step 1: Eliminate the variable from one side.
    We want to get all terms involving x x on one side and constant terms on the other side. First, subtract 2x 2x from both sides of the equation to eliminate x x from the right side.

    3x+52x=2x+202x 3x + 5 - 2x = 2x + 20 - 2x

    This simplifies to:

    x+5=20 x + 5 = 20

  • Step 2: Simplify the equation.
    Now, we need to isolate x x by removing the constant term from the left side. Subtract 5 from both sides:

    x+55=205 x + 5 - 5 = 20 - 5

    This simplifies to:

    x=15 x = 15

  • Step 3: Verify the solution.
    Substitute x=15 x = 15 back into the original equation to check if it holds true:

    3(15)+5=2(15)+20 3(15) + 5 = 2(15) + 20

    This results in:

    45+5=30+20 45 + 5 = 30 + 20

    50=50 50 = 50

    Since both sides of the equation are equal,x=15 x = 15 is indeed the correct solution.

Therefore, the solution to the equation 3x+5=2x+20 3x + 5 = 2x + 20 is x=15 x = 15 .

3

Final Answer

15 15

Key Points to Remember

Essential concepts to master this topic
  • Rule: Collect all x terms on one side, constants on other
  • Technique: Subtract 2x from both sides: 3x - 2x = x
  • Check: Substitute x = 15: 3(15) + 5 = 2(15) + 20 = 50 ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting from only one side
    Don't subtract 2x from just the left side = unbalanced equation! This violates the fundamental rule of equality and gives completely wrong answers. Always perform the same operation on both sides of the equation.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why do I subtract 2x instead of 3x?

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You want to eliminate the smaller x term to avoid negative coefficients! Subtracting 2x from both sides gives you x+5=20 x + 5 = 20 , which is easier to solve than 5=x+20 5 = -x + 20 .

Can I subtract 5 first instead of 2x?

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Yes! You can subtract 5 from both sides first to get 3x=2x+15 3x = 2x + 15 , then subtract 2x. The order doesn't matter as long as you do the same thing to both sides.

What if I get a negative answer?

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Negative answers are completely normal in algebra! Always double-check by substituting back into the original equation. If both sides match, your negative answer is correct.

How do I know which variable term to eliminate?

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Look for the smaller coefficient. In 3x+5=2x+20 3x + 5 = 2x + 20 , subtract the 2x term because 2 < 3. This keeps your x coefficient positive and makes solving easier.

Do I always need to verify my answer?

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Always verify! Substituting your answer back into the original equation catches arithmetic errors and confirms your solution is correct. It only takes 30 seconds and prevents wrong answers.

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