Solve Linear Equation: 4x - 6.9 = 2.2x + 5

Q: Why do I get a mixed number instead of a decimal?

Both forms are correct! $ 6\frac{11}{18} $ and 6.611... are the same value. Mixed numbers are often preferred because they show the exact fractional part without rounding.

Q: What if I made an error with the decimal arithmetic?

Always check your work! When you subtract 2.2x from 4x, you should get 1.8x, not 1.2x or 2.2x. Use a calculator if needed for decimal operations.

Q: Can I solve this by clearing decimals first?

Yes! Multiply the entire equation by 10 to get $ 40x - 69 = 22x + 50 $. This eliminates decimals but gives the same final answer.

Q: How do I verify my answer is correct?

Substitute $ x = 6\frac{11}{18} $ into the original equation. Calculate both sides: Left side: $ 4(6\frac{11}{18}) - 6.9 $ and Right side: $ 2.2(6\frac{11}{18}) + 5 $. They should be equal!

Linear Equations with Decimal Coefficients

$4x-6.9=2.2x+5$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 will have only the unknown X

00:33 Let's isolate the unknown X

00:45 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$4x-6.9=2.2x+5$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the equation and its components. The equation is $4x - 6.9 = 2.2x + 5$ .
Step 2: Move the terms involving $x$ to one side of the equation. Subtract $2.2x$ from both sides:
$4x - 2.2x - 6.9 = 5$ .
Step 3: Combine like terms on the left side:
$1.8x - 6.9 = 5$ .
Step 4: Move constant terms to the other side by adding $6.9$ to both sides:
$1.8x = 5 + 6.9$ .
Step 5: Simplify the equation on the right side:
$1.8x = 11.9$ .
Step 6: Solve for $x$ by dividing both sides by $1.8$ :
$x = \frac{11.9}{1.8}$ .
Step 7: Simplify the fraction if possible:
Converting $\frac{11.9}{1.8}$ to a mixed number, $x = 6\frac{11}{18}$ .

Therefore, the solution to the equation is $x = 6\frac{11}{18}$ .

Final Answer

$x=6\frac{11}{18}$

Key Points to Remember

Essential concepts to master this topic

Isolation: Move all x terms to one side, constants to other
Technique: Subtract 2.2x from both sides: 4x - 2.2x = 1.8x
Check: Substitute $x = 6\frac{11}{18}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Forgetting to subtract decimal coefficients correctly
Don't calculate 4x - 2.2x = 2.2x instead of 1.8x! This leads to dividing by the wrong coefficient and getting the wrong answer. Always double-check decimal arithmetic when combining like terms.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I get a mixed number instead of a decimal?

Both forms are correct! $6\frac{11}{18}$ and 6.611... are the same value. Mixed numbers are often preferred because they show the exact fractional part without rounding.

How do I convert 11.9/1.8 to a mixed number?

First divide: 11.9 ÷ 1.8 = 6.611... The whole part is 6. Then convert the decimal 0.611... to a fraction: multiply both numerator and denominator by 10 to get $\frac{11}{18}$ .

What if I made an error with the decimal arithmetic?

Always check your work! When you subtract 2.2x from 4x, you should get 1.8x, not 1.2x or 2.2x. Use a calculator if needed for decimal operations.

Can I solve this by clearing decimals first?

Yes! Multiply the entire equation by 10 to get $40x - 69 = 22x + 50$ . This eliminates decimals but gives the same final answer.

How do I verify my answer is correct?

Substitute $x = 6\frac{11}{18}$ into the original equation. Calculate both sides: Left side: $4(6\frac{11}{18}) - 6.9$ and Right side: $2.2(6\frac{11}{18}) + 5$ . They should be equal!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime