Solve for X in 0.7x + 0.5 = -0.3x: Linear Equation Solution

Linear Equations with Decimal Coefficients

Find the value of the parameter X

0.7x+0.5=0.3x 0.7x+\text{0}.5=-0.3x

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:04 Isolate the unknown X
00:28 Reduce
00:38 Convert from negative to positive
00:50 A negative multiplied by a negative always equals a positive
00:53 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the value of the parameter X

0.7x+0.5=0.3x 0.7x+\text{0}.5=-0.3x

2

Step-by-step solution

To solve the problem, let's go through the steps:

First, we start with the given equation:

0.7x+0.5=0.3x 0.7x + 0.5 = -0.3x

To isolate x x , we will first combine all the x x -terms on one side. We do this by adding 0.3x 0.3x to both sides of the equation:

0.7x+0.3x+0.5=0 0.7x + 0.3x + 0.5 = 0

This simplifies to:

1x+0.5=0 1x + 0.5 = 0 or x+0.5=0 x + 0.5 = 0

Next, we isolate x x by subtracting 0.5 0.5 from both sides:

x=0.5 x = -0.5

Therefore, the solution to the problem is x=0.5 x = -0.5 .

3

Final Answer

0.5 -0.5

Key Points to Remember

Essential concepts to master this topic
  • Collection Rule: Combine all x-terms on one side of equation
  • Technique: Add 0.3x to both sides: 0.7x + 0.3x = 1x
  • Check: Substitute x = -0.5: 0.7(-0.5) + 0.5 = -0.35 + 0.5 = 0.15 ≠ -0.3(-0.5) = 0.15 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to add terms to both sides equally
    Don't add 0.3x to only the left side = unbalanced equation! This violates the fundamental rule that whatever you do to one side, you must do to the other. Always perform the same operation on both sides of the equation.

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 need to move all the x-terms to one side?

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Moving all x-terms to one side combines like terms and makes it easier to solve. In this problem, we get 0.7x+0.3x=1x 0.7x + 0.3x = 1x , which is much simpler to work with!

What if I move the x-terms to the right side instead?

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That works too! You'd subtract 0.7x from both sides to get 0.5=0.3x0.7x=1x 0.5 = -0.3x - 0.7x = -1x . Then divide by -1 to get x=0.5 x = -0.5 - same answer!

How do I handle the decimal numbers?

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Treat decimal coefficients just like whole numbers! The key is to combine like terms carefully: 0.7x+0.3x=1.0x=x 0.7x + 0.3x = 1.0x = x .

Can I multiply everything by 10 to eliminate decimals?

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Yes! Multiplying by 10 gives you 7x+5=3x 7x + 5 = -3x , which is easier for some students. Just remember to multiply every single term by 10.

How do I check if x = -0.5 is correct?

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Substitute back into the original equation: Left side = 0.7(0.5)+0.5=0.35+0.5=0.15 0.7(-0.5) + 0.5 = -0.35 + 0.5 = 0.15 . Right side = 0.3(0.5)=0.15 -0.3(-0.5) = 0.15 . Since both sides equal 0.15, our answer is correct!

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