Solve the Linear Equation: -3(x+4) - 5x + 5 = 3 - 4(x-2) + 5x

Q: How do I keep track of negative signs when distributing?

Write each step carefully! For $ -3(x+4) $, think: negative 3 times x equals negative 3x, and negative 3 times positive 4 equals negative 12.

Q: What if I get the same variable term on both sides?

That's normal! Move all variable terms to one side by adding or subtracting. In this problem, we added $ 8x $ to both sides to collect all x-terms on the right.

Q: How can I check my work without substituting?

You can work backwards! Start with $ x = -2 $ and see if you can build back to the original equation, but substitution is usually faster and more reliable.

Q: Why did we get a negative answer?

Negative solutions are completely normal! The equation determines the answer, not our preferences. Always trust your algebra steps and verify with substitution.

Linear Equations with Distributive Property

Solve for X:

$-3(x+4)-5x+5=3-4(x-2)+5x$

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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

00:22 Collect like terms

00:49 Arrange the equation so that X is isolated on one side

01:07 Collect like terms

01:13 Isolate X

01:21 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:

$-3(x+4)-5x+5=3-4(x-2)+5x$

Step-by-step solution

To solve this equation, we will break it down into simpler steps:

$-3(x+4)-5x+5=3-4(x-2)+5x$

Step 1: Apply the distributive property to both sides.
Left Side: $-3(x+4) = -3x - 12$
So, $-3(x+4)-5x+5 = -3x - 12 - 5x + 5$
Right Side: $-4(x-2) = -4x + 8$
So, $3 - 4(x-2) + 5x = 3 - 4x + 8 + 5x$
Step 2: Simplify both sides by combining like terms.
Left Side: Combine like terms $-3x - 5x - 12 + 5 = -8x - 7$
Right Side: Combine like terms $-4x + 5x + 3 + 8 = x + 11$
Step 3: Set the simplified forms equal: $-8x - 7 = x + 11$
Step 4: Solve for $x$ by manipulating the equation:
Add $8x$ to both sides: $-7 = 9x + 11$
Subtract 11 from both sides: $-18 = 9x$
Divide by 9: $x = -2$

Therefore, the solution to the problem is $x = -2$ , which matches choice 2.

Final Answer

-2

Key Points to Remember

Essential concepts to master this topic

Distribution: Apply distributive property to both parentheses first
Technique: Combine like terms: $-3x - 5x = -8x$
Check: Substitute $x = -2$ : both sides equal 27 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute negative signs
Don't distribute $-3(x+4)$ as $-3x + 12$ = wrong signs! This creates a positive 12 instead of negative 12, throwing off your entire solution. Always distribute the negative to both terms: $-3x - 12$ .

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 first instead of combining like terms?

You can't combine terms that are inside parentheses with terms outside! Parentheses act like walls - you must break them down with distribution before combining anything.

How do I keep track of negative signs when distributing?

Write each step carefully! For $-3(x+4)$ , think: negative 3 times x equals negative 3x, and negative 3 times positive 4 equals negative 12.

What if I get the same variable term on both sides?

That's normal! Move all variable terms to one side by adding or subtracting. In this problem, we added $8x$ to both sides to collect all x-terms on the right.

How can I check my work without substituting?

You can work backwards! Start with $x = -2$ and see if you can build back to the original equation, but substitution is usually faster and more reliable.

Why did we get a negative answer?

Negative solutions are completely normal! The equation determines the answer, not our preferences. Always trust your algebra steps and verify with substitution.

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