Solve for X in the Linear Equation: 8.15x - 13.14 + 5 = 7.1 - 8.4x

Linear Equations with Decimal Coefficients

Solve for X:


8.15x13.14+5=7.18.4x 8.15x-13.14+5=7.1-8.4x

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:05 Collect terms
00:18 Arrange the equation so that one side has only the unknown X
00:44 Collect terms
00:58 Isolate X
01:17 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:


8.15x13.14+5=7.18.4x 8.15x-13.14+5=7.1-8.4x

2

Step-by-step solution

Let's solve the given equation 8.15x13.14+5=7.18.4x 8.15x - 13.14 + 5 = 7.1 - 8.4x step by step:

Step 1: Simplify both sides of the equation.
On the left-hand side, combine like terms:

8.15x13.14+5=8.15x8.14 8.15x - 13.14 + 5 = 8.15x - 8.14

Step 2: Simplify the right-hand side:

7.18.4x 7.1 - 8.4x (no combining needed here).

Now the equation is:

8.15x8.14=7.18.4x 8.15x - 8.14 = 7.1 - 8.4x

Step 3: Move all x x -terms to one side and constant terms to the other side.
Add 8.4x 8.4x to both sides:

8.15x+8.4x8.14=7.1 8.15x + 8.4x - 8.14 = 7.1

16.55x8.14=7.1 16.55x - 8.14 = 7.1

Step 4: Move the constant term on the left to the right side by adding 8.14:

16.55x=7.1+8.14 16.55x = 7.1 + 8.14

16.55x=15.24 16.55x = 15.24

Step 5: Solve for x x by dividing both sides by 16.55:

x=15.2416.55 x = \frac{15.24}{16.55}

x0.92 x \approx 0.92

Therefore, the solution to the equation is x=0.92 x = 0.92 .

3

Final Answer

0.92 0.92

Key Points to Remember

Essential concepts to master this topic
  • Combine Terms: Simplify constants on each side before moving variables
  • Collect Variables: Move all x-terms to one side: 8.15x + 8.4x = 16.55x
  • Verify Solution: Substitute x = 0.92 back into original equation ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to combine like terms first
    Don't jump straight to moving variables without simplifying -13.14 + 5 = -8.14 first! This creates calculation errors and wrong coefficients. Always combine like terms on each side before collecting variables.

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 need to combine -13.14 + 5 first?

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Combining like terms first makes the equation simpler to work with. If you skip this step, you'll have more terms to track and higher chance of making errors!

What's the best way to move all the x-terms to one side?

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Add 8.4x 8.4x to both sides to get all x-terms on the left. This gives you 16.55x 16.55x on one side and just numbers on the other.

How can I check if x = 0.92 is correct?

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Substitute back into the original equation: 8.15(0.92)13.14+5 8.15(0.92) - 13.14 + 5 should equal 7.18.4(0.92) 7.1 - 8.4(0.92) . Both sides should give you the same value!

What if my decimal answer doesn't come out exactly?

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That's normal with decimal coefficients! Round to a reasonable number of decimal places (usually 2-3) and always check your work by substituting back.

Is there a shortcut for decimal equations?

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You can multiply everything by 100 to eliminate decimals first, but be careful with the arithmetic. The standard method of combining terms then collecting variables is usually more reliable.

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