Solve for X: -7(2x+3)-4(x+2)=5(2-3x) | Linear Equation Practice

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

Distribution must come first! You can't combine terms that are still trapped inside parentheses. Think of it like unpacking boxes before organizing - you need to see all the pieces first.

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

Write out each multiplication step: $ -7(2x+3) = (-7 \times 2x) + (-7 \times 3) = -14x - 21 $. This prevents sign errors that lead to wrong answers!

Q: What if I get confused with all the x terms?

Collect all x terms on one side and numbers on the other. In this problem: -18x and +15x go together, while -29 and +10 go together.

Q: How can I check if x = -13 is really correct?

Substitute back into the original equation: $ -7(2(-13)+3)-4((-13)+2) $ should equal $ 5(2-3(-13)) $. Both sides should give you the same number!

Q: Why did we move +15x to the left side instead of -18x to the right?

Either way works! The goal is to get all x terms on one side. Moving +15x left gives $ -3x = 39 $, which is easier than moving -18x right to get $ 39 = 3x $.

Linear Equations with Multi-Step Distribution

Solve for x:

$-7(2x+3)-4(x+2)=5(2-3x)$

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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

00:30 Combine like terms

00:44 Arrange the equation so that only the unknown X is on one side

01:01 Combine like terms

01:08 Isolate X

01:16 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

Solve for x:

$-7(2x+3)-4(x+2)=5(2-3x)$

Step-by-step solution

To open parentheses we will use the formula:

$a\left(x+b\right)=ax+ab$

$(-7\times2x)+(-7\times3)+(-4\times x)+(-4\times2)=(5\times2)+(5\times-3x)$

We multiply accordingly:

$-14x-21-4x-8=10-15x$

We calculate the elements in the left section:

$-18x-29=10-15x$

In the left section we enter the elements with the X and in the right section those without the X, remember to change the plus and minus signs as appropriate when transferring:

$-18x+15x=10+29$

We calculate the elements accordingly:

$-3x=39$

We divide the two sections by -3:

$\frac{-3x}{-3}=\frac{39}{-3}$

$x=-13$

Final Answer

-13

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply distributive property to each parentheses first
Technique: Combine like terms: -14x - 4x = -18x on left side
Check: Substitute x = -13 into original equation to verify both sides equal ✓

Common Mistakes

Avoid these frequent errors

Not distributing negative signs correctly
Don't forget to distribute the negative sign to every term = wrong signs throughout! When you have -7(2x+3), the negative must multiply both 2x AND 3. Always distribute the negative sign to each term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=1 $$

What is the value of x?

FAQ

Everything you need to know about this question

Why do I need to distribute before combining like terms?

Distribution must come first! You can't combine terms that are still trapped inside parentheses. Think of it like unpacking boxes before organizing - you need to see all the pieces first.

How do I keep track of negative signs when distributing?

Write out each multiplication step: $-7(2x+3) = (-7 \times 2x) + (-7 \times 3) = -14x - 21$ . This prevents sign errors that lead to wrong answers!

What if I get confused with all the x terms?

Collect all x terms on one side and numbers on the other. In this problem: -18x and +15x go together, while -29 and +10 go together.

How can I check if x = -13 is really correct?

Substitute back into the original equation: $-7(2(-13)+3)-4((-13)+2)$ should equal $5(2-3(-13))$ . Both sides should give you the same number!

Why did we move +15x to the left side instead of -18x to the right?

Either way works! The goal is to get all x terms on one side. Moving +15x left gives $-3x = 39$ , which is easier than moving -18x right to get $39 = 3x$ .

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