Solve for X in the Equation: 6x + 3.4 = 15.4

Linear Equations with Decimal Constants

Solve for X:

6x+3.4=15.4 6x+3.4=15.4

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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
00:27 Let's isolate the unknown X and calculate
00:38 Let's simplify what we can
00:42 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:

6x+3.4=15.4 6x+3.4=15.4

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Subtract 3.4 from both sides of the equation.
  • Step 2: Divide the resulting value by 6 to find x x .

Let's execute each step:
Step 1: The original equation is 6x+3.4=15.4 6x + 3.4 = 15.4 .
Subtract 3.4 from both sides:
6x+3.43.4=15.43.4 6x + 3.4 - 3.4 = 15.4 - 3.4
This simplifies to:
6x=12 6x = 12 .

Step 2: Divide both sides by 6 to solve for x x :
x=126 x = \frac{12}{6} .
This simplifies to:
x=2 x = 2 .

Therefore, the solution to the problem is x=2 x = 2 , which matches choice 3.

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Isolation Strategy: Remove constants first, then eliminate coefficients
  • Technique: Subtract 3.4 from both sides: 15.4 - 3.4 = 12
  • Check: Substitute back: 6(2) + 3.4 = 12 + 3.4 = 15.4 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing before subtracting the constant term
    Don't divide 15.4 by 6 first = 2.57, then try to work with decimals! This ignores the addition and creates messy calculations. Always subtract the constant term first to isolate the variable term.

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 do I subtract 3.4 from both sides instead of dividing first?

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You follow the reverse order of operations! Since addition was the last operation applied to x, you undo it first. Think of it as peeling an onion - remove the outer layer (addition) before the inner layer (multiplication).

What if I get confused about which operation to do first?

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Look at what's happening to the variable x. Here, x is multiplied by 6, then 3.4 is added. To solve, do the opposite in reverse order: subtract first, then divide!

Do I need to worry about the decimals making this harder?

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Not at all! Decimals work exactly like whole numbers in equations. 15.4 - 3.4 = 12 is just as straightforward as any subtraction you've done before.

How can I double-check my arithmetic with decimals?

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Use the substitution check: Replace x with your answer in the original equation. Calculate 6(2)+3.4 6(2) + 3.4 step by step: 12 + 3.4 = 15.4. It matches the right side!

What if my answer doesn't come out to a nice whole number?

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That's completely normal! Many equations have fractional or decimal answers. The key is following the correct steps - the answer will be whatever it needs to be.

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