Solve Linear Equation: Finding X in -3.5x + 4.2 = 3.72

Linear Equations with Decimal Coefficients

Solve for X:

−3.5x+4.2=3.72 -3.5x+4.2=3.72

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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
00:08 Let's arrange the equation so that one side has only the unknown X
00:23 Let's simplify what we can
00:33 Let's isolate the unknown X and calculate
00:52 Let's simplify what we can
01:00 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:

−3.5x+4.2=3.72 -3.5x+4.2=3.72

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Subtract the constant term from both sides of the equation.
  • Step 2: Divide by the coefficient of x x to solve for the variable.

Let's apply these steps to the equation −3.5x+4.2=3.72-3.5x + 4.2 = 3.72:

Step 1: Subtract 4.2 from both sides of the equation:
−3.5x+4.2−4.2=3.72−4.2-3.5x + 4.2 - 4.2 = 3.72 - 4.2
This simplifies to:
−3.5x=−0.48-3.5x = -0.48

Step 2: Divide both sides by −3.5-3.5 to isolate x x :
x=−0.48−3.5 x = \frac{-0.48}{-3.5}

Perform the division:
x=0.137 x = 0.137

Therefore, the solution to the problem is x=0.137 x = 0.137 .

3

Final Answer

0.137

Key Points to Remember

Essential concepts to master this topic
  • Isolation Strategy: Subtract constants first, then divide by coefficient
  • Technique: From −3.5x=−0.48-3.5x = -0.48, divide: x=−0.48−3.5=0.137x = \frac{-0.48}{-3.5} = 0.137
  • Check: Substitute back: −3.5(0.137)+4.2=3.72-3.5(0.137) + 4.2 = 3.72 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting negative signs when dividing
    Don't divide -0.48 ÷ -3.5 and get -0.137! When dividing two negatives, the result is positive. Always remember that negative ÷ negative = positive.

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 4.2 from both sides first?

+

You want to isolate the term with x! Since 4.2 is added to −3.5x-3.5x, you subtract 4.2 from both sides to get the x-term by itself.

How do I handle the negative coefficient -3.5?

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Divide both sides by -3.5 just like any other number. Remember: when you divide a negative by a negative, you get a positive result!

Why is my answer a decimal instead of a whole number?

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That's completely normal! Not all linear equations have integer solutions. Decimal answers are just as valid as whole numbers.

How can I check if x = 0.137 is correct?

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Substitute back into the original equation: −3.5(0.137)+4.2-3.5(0.137) + 4.2. This should equal 3.72. If it does, your answer is right!

What if I get confused with the decimal arithmetic?

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Take it step by step! First subtract: 3.72−4.2=−0.483.72 - 4.2 = -0.48. Then divide: −0.48÷(−3.5)=0.137-0.48 ÷ (-3.5) = 0.137. Use a calculator if needed.

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