Solve for X in the Linear Equation: 10 + 3x = 19

Linear Equations with Two-Step Solutions

Solve for X:

10+3x=19 10+3x=19

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to isolate the unknown X
00:07 Let's arrange the equation so that one side has only the unknown X
00:19 Let's simplify what we can
00:28 Let's isolate the unknown X and calculate
00:43 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:

10+3x=19 10+3x=19

2

Step-by-step solution

To solve the equation 10+3x=1910 + 3x = 19, follow these steps:

  • Step 1: Subtract 10 from both sides of the equation to begin isolating xx:
  • 10+3x10=191010 + 3x - 10 = 19 - 10
  • This simplifies to 3x=93x = 9.
  • Step 2: Divide both sides by 3 to solve for xx:
  • 3x3=93\frac{3x}{3} = \frac{9}{3}
  • This reduces to x=3x = 3.

Therefore, the solution to the problem is x=3x = 3.

3

Final Answer

3

Key Points to Remember

Essential concepts to master this topic
  • Rule: Isolate the variable term before dividing by coefficient
  • Technique: Subtract 10 first: 10 + 3x - 10 = 19 - 10
  • Check: Substitute back: 10 + 3(3) = 10 + 9 = 19 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing by coefficient before isolating variable term
    Don't divide 3x by 3 while it's still added to 10 = incomplete isolation! This leaves you with x + 10/3 instead of solving for x. Always subtract or add constants first to isolate the variable term completely.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( x - 3 + 5 = 8 - 2 \)

FAQ

Everything you need to know about this question

Why can't I divide everything by 3 right away?

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You need to isolate the variable term first! If you divide the entire equation 10+3x=19 10 + 3x = 19 by 3, you get messy fractions. Always handle addition and subtraction before multiplication and division.

What's the difference between 3x and x + 3?

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3x means 3 times x (multiplication), while x + 3 means x plus 3 (addition). In 10+3x=19 10 + 3x = 19 , the 3 is multiplied by x, so you divide by 3 to undo it.

Do I always subtract the constant term first?

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In equations like 10+3x=19 10 + 3x = 19 , yes! You want to get the variable term by itself on one side. Use inverse operations: if 10 is added, subtract 10 from both sides.

How do I check my work without making mistakes?

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Substitute your answer back into the original equation. For x = 3: 10+3(3)=10+9=19 10 + 3(3) = 10 + 9 = 19 . Both sides equal 19, so the answer is correct!

What if I get a negative answer?

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Negative solutions are completely normal! Just follow the same steps carefully. Always double-check your arithmetic, especially with negative numbers.

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