Solve for X in 17.6-x=-11.3: Linear Equation with Decimals

Linear Equations with Decimal Subtraction

17.6−x=−11.3 17.6-x=-11.3

x=? x=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's isolate the unknown X, and calculate
00:14 We'll use long addition for calculation
00:23 Convert from negative to positive
00:26 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

17.6−x=−11.3 17.6-x=-11.3

x=? x=\text{?}

2

Step-by-step solution

Let's solve the equation 17.6−x=−11.3 17.6 - x = -11.3 step by step:

  • Step 1: Identify the need to isolate x x on one side. We currently have 17.6−x=−11.3 17.6 - x = -11.3 .
  • Step 2: To isolate x x , add x x to both sides of the equation, resulting in 17.6=x−11.3 17.6 = x - 11.3 .
  • Step 3: Now, add 11.3 11.3 to both sides to solve for x x :
    17.6+11.3=x−11.3+11.3 17.6 + 11.3 = x - 11.3 + 11.3 . This simplifies further to 28.9=x 28.9 = x .

Therefore, the solution to the equation is x=28.9 x = 28.9 .

3

Final Answer

28.9 28.9

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Move terms to opposite sides to isolate variable
  • Technique: Add x to both sides: 17.6 = x - 11.3
  • Check: Substitute 28.9: 17.6 - 28.9 = -11.3 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting 17.6 from both sides first
    Don't subtract 17.6 from both sides getting -x = -28.9! This creates a negative variable that's harder to work with. Always add x to both sides first to keep the variable positive, then solve normally.

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 add x to both sides instead of subtracting 17.6?

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Adding x to both sides gives you 17.6 = x - 11.3, which keeps the variable positive. This is easier to work with than -x = -28.9 where you'd need to divide by -1.

What if I forget to change the sign when moving terms?

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Remember the golden rule: when you move a term across the equals sign, change its sign! Moving -x becomes +x, moving -11.3 becomes +11.3.

How can I check my decimal arithmetic?

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For 17.6+11.3 17.6 + 11.3 , line up the decimal points: 17.6 + 11.3 = 28.9. Then substitute back to verify your answer works!

What if my answer has more decimal places?

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That's normal! Some linear equations give answers like x = 3.75 or x = -2.333.... Just be careful with your decimal arithmetic and always check your work.

Is there a faster way to solve this type of equation?

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Yes! Once you recognize the pattern a−x=b a - x = b , you can jump straight to x=a−b x = a - b . For this problem: x=17.6−(−11.3)=17.6+11.3=28.9 x = 17.6 - (-11.3) = 17.6 + 11.3 = 28.9 .

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