Solve for X in the Linear Equation: 5x + 10 = 3x + 18

Linear Equations with Variable Isolation

Solve for X:

5x+10=3x+18 5x + 10 = 3x + 18

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1

Understand the problem

Solve for X:

5x+10=3x+18 5x + 10 = 3x + 18

2

Step-by-step solution

To solve the equation 5x+10=3x+18 5x + 10 = 3x + 18 , follow these steps:

1. Subtract 3x 3x from both sides to get:

5x3x+10=18 5x - 3x + 10 = 18

2. Simplify the equation:

2x+10=18 2x + 10 = 18

3. Subtract 10 10 from both sides:

2x=8 2x = 8

4. Divide both sides by 2 2 :

x=4 x = 4

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Move all terms with variables to one side first
  • Technique: Subtract 3x 3x from both sides: 5x3x=2x 5x - 3x = 2x
  • Check: Substitute x = 4: 5(4)+10=3(4)+18=30 5(4) + 10 = 3(4) + 18 = 30

Common Mistakes

Avoid these frequent errors
  • Moving terms incorrectly across the equal sign
    Don't just move 3x 3x to the left and keep it positive = 5x+3x+10=18 5x + 3x + 10 = 18 ! This gives x=1 x = 1 instead of the correct answer. Always change the sign when moving terms across the equal sign.

Practice Quiz

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\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why do I subtract 3x from both sides instead of adding it?

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You want to collect all x terms on one side. Since you have +3x +3x on the right, you subtract 3x 3x from both sides to move it to the left side as 3x -3x .

Can I subtract 5x from both sides instead?

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Absolutely! You'd get 10=2x+18 10 = -2x + 18 , then 8=2x -8 = -2x , so x=4 x = 4 . Both approaches work - choose whichever feels easier!

What if I get a negative coefficient for x?

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No problem! Just divide both sides by the negative number. For example, if you get 2x=8 -2x = -8 , divide both sides by 2 -2 to get x=4 x = 4 .

How do I know which side to move the variables to?

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It doesn't matter! You can move all variables to either side. Most students find it easier to move them to the side with the larger coefficient to avoid negative numbers.

Do I always subtract constants last?

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Yes! Always handle variables first, then constants. This keeps your work organized: collect like terms, then isolate the variable by dealing with any remaining numbers.

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