Solve for X: -3(x+1)+5x-4=-3+5(x-1) | Step-by-Step Guide

Q: Why do I get a fraction instead of a whole number?

Not all equations have whole number solutions! Fractions are perfectly valid answers. The equation $ -3(x+1)+5x-4=-3+5(x-1) $ naturally leads to $ x = \frac{1}{3} $.

Q: How do I handle the negative sign in -3(x+1)?

The negative distributes to every term inside: $ -3(x+1) = -3x - 3 $. Don't forget that negative times positive equals negative!

Q: What's the easiest way to combine like terms?

Group similar terms together: x terms: $ -3x + 5x = 2x $Constants: $ -3 - 4 = -7 $ This keeps your work organized!

Q: How can I check if x = 1/3 is correct?

Substitute back into the original equation. Left side: $ -3(\frac{1}{3}+1)+5(\frac{1}{3})-4 = -4 + \frac{5}{3} - 4 = -\frac{19}{3} $. Right side should equal the same value!

Q: Why do I move x terms to one side?

Isolation strategy! Moving all x terms to one side (like $ 2x - 5x = -3x $) lets you factor out x and solve directly. It's much cleaner than having x on both sides.

Linear Equations with Fractional Solutions

Solve for x:

$-3(x+1)+5x-4=-3+5(x-1)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 Open parentheses properly, multiply by each factor

00:29 Collect like terms

00:54 Arrange the equation so that X is isolated on one side

01:10 Collect like terms

01:16 Isolate X

01:24 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:

$-3(x+1)+5x-4=-3+5(x-1)$

Step-by-step solution

First, we will expand the parentheses on both sides:

$-3x-3+5x-4=-3+5x-5$

Enter the like terms in both sections. Let's start with the left section:

$-3x+5x=2x$

$-3-4=-7$

Calculate the like terms on the right side:

$-3-5=-8$

Now, we obtain the equation:

$2x-7=-8+5x$

To the right side we will move the members without the X, while to the left side we move those with the X, keeping the plus and minus signs as appropriate:

$2x-5x=-8+7$

$-3x=-1$

Finally, we divide both sides by -3:

$\frac{-1}{-3}=\frac{-3x}{-3}$

$\frac{1}{3}=x$

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Expand parentheses first before combining like terms
Technique: Move x terms left, constants right: 2x - 5x = -8 + 7
Check: Substitute $\frac{1}{3}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute negative signs correctly
Don't just distribute the coefficient and ignore the negative sign = wrong signs throughout! This creates errors in every step. Always distribute both the coefficient AND the sign 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 get a fraction instead of a whole number?

Not all equations have whole number solutions! Fractions are perfectly valid answers. The equation $-3(x+1)+5x-4=-3+5(x-1)$ naturally leads to $x = \frac{1}{3}$ .

How do I handle the negative sign in -3(x+1)?

The negative distributes to every term inside: $-3(x+1) = -3x - 3$ . Don't forget that negative times positive equals negative!

What's the easiest way to combine like terms?

Group similar terms together:

x terms: $-3x + 5x = 2x$
Constants: $-3 - 4 = -7$

This keeps your work organized!

How can I check if x = 1/3 is correct?

Substitute back into the original equation. Left side: $-3(\frac{1}{3}+1)+5(\frac{1}{3})-4 = -4 + \frac{5}{3} - 4 = -\frac{19}{3}$ . Right side should equal the same value!

Why do I move x terms to one side?

Isolation strategy! Moving all x terms to one side (like $2x - 5x = -3x$ ) lets you factor out x and solve directly. It's much cleaner than having x on both sides.

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