Solve for X in -8x + 3 + 1/5 = -7x + 5(1-x): Linear Equation Challenge

Q: Why do I need to distribute 5(1-x) first?

You must distribute before combining like terms! The expression 5(1-x) means 5×1 + 5×(-x) = 5 - 5x. If you skip this step, you can't properly collect the x terms together.

Q: How do I add fractions like 3 + 1/5?

Convert to the same denominator: $ 3 = \frac{15}{5} $, so $ 3 + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5} $. Always find a common denominator first!

Q: What's the difference between -7x and -5x when collecting terms?

After distributing, you have -7x - 5x = -12x on the right side. Don't forget the negative sign when distributing: 5(1-x) = 5 - 5x, not 5 + 5x.

Q: Why is my final answer a fraction?

That's completely normal! When you solve $ 4x = \frac{9}{5} $, dividing gives $ x = \frac{9}{5} ÷ 4 = \frac{9}{20} $. Many linear equations have fractional solutions.

Q: How can I check if x = 9/20 is correct?

Substitute back into the original equation: $ -8(\frac{9}{20}) + 3 + \frac{1}{5} $ should equal $ -7(\frac{9}{20}) + 5(1-\frac{9}{20}) $. Both sides should give you the same decimal value!

Linear Equations with Distribution and Fractions

Solve for x:

$-8x+3+\frac{1}{5}=-7x+5(1-x)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Group like terms

00:11 Expand brackets properly, multiply by each term

00:25 Group like terms

00:28 Arrange the equation so that one side contains only the unknown X

00:49 Group like terms

00:52 Find the common denominator

00:59 Isolate X

01:05 Make sure to multiply numerator by numerator and denominator by denominator

01:08 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$-8x+3+\frac{1}{5}=-7x+5(1-x)$

Step-by-step solution

To solve the equation $-8x + 3 + \frac{1}{5} = -7x + 5(1-x)$ , follow these steps:

Step 1: Simplify the right-hand side by distributing the 5: $-7x + 5(1-x) = -7x + 5 - 5x$ .
Step 2: This leads to $-8x + 3 + \frac{1}{5} = -12x + 5$ .
Step 3: Combine like terms on both sides. The left simplifies to $-8x + \frac{16}{5}$ and the right side already simplified as stated.
Step 4: Move all terms involving $x$ to one side, and constants to the other: Add $12x$ to both sides to get $12x - 8x = 5 - \frac{16}{5}$ .
Step 5: Simplify the equation: $4x = \frac{25}{5} - \frac{16}{5} = \frac{9}{5}$ .
Step 6: Solve for $x$ by dividing both sides by 4: $x = \frac{9}{20}$ .

Therefore, the solution to the problem is $x = \frac{9}{20}$ .

Final Answer

$\frac{9}{20}$

Key Points to Remember

Essential concepts to master this topic

Distribution First: Expand 5(1-x) before combining like terms
Technique: Convert $3 + \frac{1}{5} = \frac{16}{5}$ using common denominators
Check: Substitute $x = \frac{9}{20}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the 5 to both terms
Don't write 5(1-x) = 5-x! This misses distributing to the x term, giving 5-x instead of 5-5x. This leads to collecting wrong like terms and getting x = 16 instead of x = 9/20. Always distribute the coefficient to every term inside parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I need to distribute 5(1-x) first?

You must distribute before combining like terms! The expression 5(1-x) means 5×1 + 5×(-x) = 5 - 5x. If you skip this step, you can't properly collect the x terms together.

How do I add fractions like 3 + 1/5?

Convert to the same denominator: $3 = \frac{15}{5}$ , so $3 + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5}$ . Always find a common denominator first!

What's the difference between -7x and -5x when collecting terms?

After distributing, you have -7x - 5x = -12x on the right side. Don't forget the negative sign when distributing: 5(1-x) = 5 - 5x, not 5 + 5x.

Why is my final answer a fraction?

That's completely normal! When you solve $4x = \frac{9}{5}$ , dividing gives $x = \frac{9}{5} ÷ 4 = \frac{9}{20}$ . Many linear equations have fractional solutions.

How can I check if x = 9/20 is correct?

Substitute back into the original equation: $-8(\frac{9}{20}) + 3 + \frac{1}{5}$ should equal $-7(\frac{9}{20}) + 5(1-\frac{9}{20})$ . Both sides should give you the same decimal value!

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