Solve for X: -7(x+4)-2=5(2-x) Linear Equation Solution

Q: Why do I need to distribute before combining like terms?

You must distribute first because parentheses create grouped terms that need to be expanded. Trying to combine like terms while parentheses are still there leads to confusion and errors.

Q: How do I handle the negative sign in front of 7?

The negative sign affects everything inside the parentheses! So $ -7(x+4) = -7x + (-7)(4) = -7x - 28 $. Don't forget that negative times positive equals negative.

Q: What's the best way to keep track of all the terms?

Write each step clearly on a new line. After distributing, underline like terms with the same color or symbol to help you combine them correctly.

Q: Why did we add 5x to both sides instead of subtracting?

We had $ -7x $ on the left and $ -5x $ on the right. Adding $ +5x $ to both sides eliminates the negative 5x on the right and gives us $ -2x $ on the left.

Q: How can I check if x = -20 is really correct?

Substitute $ x = -20 $ into the original equation: $ -7(-20+4)-2 $ and $ 5(2-(-20)) $. Both sides should equal 110!

Linear Equations with Distribution and Collection

Solve for x:

$-7(x+4)-2=5(2-x)$

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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

00:21 Combine like terms

00:31 Arrange the equation so that X is isolated on one side

00:48 Combine like terms

00:52 Isolate X

01:01 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:

$-7(x+4)-2=5(2-x)$

Step-by-step solution

To solve the equation $-7(x+4)-2=5(2-x)$ , follow these steps:

Step 1: Distribute the coefficients across the terms inside the parentheses.
On the left side: Apply $-7$ to $(x + 4)$ :
$-7 \cdot x + (-7) \cdot 4 = -7x - 28$ .
On the right side: Apply $5$ to $(2 - x)$ :
$5 \cdot 2 + 5 \cdot (-x) = 10 - 5x$ .
Step 2: Substitute the distributed expressions back into the equation:
$-7x - 28 - 2 = 10 - 5x$ .
Step 3: Simplify both sides by combining like terms:
The left side simplifies to: $-7x - 30$ .
Thus, the equation becomes: $-7x - 30 = 10 - 5x$ .
Step 4: Get all terms involving $x$ on one side of the equation:
Add $5x$ to both sides: $-7x + 5x - 30 = 10$ .
This simplifies to: $-2x - 30 = 10$ .
Step 5: Isolate the term with $x$ on one side:
Add $30$ to both sides: $-2x = 40$ .
Step 6: Solve for $x$ by dividing by $-2$ :
$x = \frac{40}{-2} = -20$ .

Therefore, the solution to the equation is $x = -20$ .

Final Answer

-20

Key Points to Remember

Essential concepts to master this topic

Distribution: Apply coefficients to all terms inside parentheses carefully
Technique: Collect like terms: $-7x + 5x = -2x$
Check: Substitute $x = -20$ : both sides equal 110 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute negative signs correctly
Don't apply -7 to just x and forget the negative affects both terms = wrong signs throughout! This creates calculation errors that compound. Always distribute the negative to every term: -7(x+4) = -7x - 28.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=0 $$

FAQ

Everything you need to know about this question

Why do I need to distribute before combining like terms?

You must distribute first because parentheses create grouped terms that need to be expanded. Trying to combine like terms while parentheses are still there leads to confusion and errors.

How do I handle the negative sign in front of 7?

The negative sign affects everything inside the parentheses! So $-7(x+4) = -7x + (-7)(4) = -7x - 28$ . Don't forget that negative times positive equals negative.

What's the best way to keep track of all the terms?

Write each step clearly on a new line. After distributing, underline like terms with the same color or symbol to help you combine them correctly.

Why did we add 5x to both sides instead of subtracting?

We had $-7x$ on the left and $-5x$ on the right. Adding $+5x$ to both sides eliminates the negative 5x on the right and gives us $-2x$ on the left.

How can I check if x = -20 is really correct?

Substitute $x = -20$ into the original equation: $-7(-20+4)-2$ and $5(2-(-20))$ . Both sides should equal 110!

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