Solve the Linear Equation: Unravel 3x + 5(x + 4) = 0

Linear Equations with Distributive Property

3x+5(x+4)=0 3x+5(x+4)=0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Open parentheses properly, multiply by each factor
00:12 Group factors
00:19 Arrange the equation so that only the unknown X is on one side
00:25 Isolate X
00:34 Factor 20 into 4 and 5
00:38 Factor 8 into 4 and 2
00:41 Reduce what we can, and substitute
00:47 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3x+5(x+4)=0 3x+5(x+4)=0

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Apply the distributive property to the equation.
  • Step 2: Combine like terms.
  • Step 3: Solve for x x .

Now, let's work through each step:

Step 1: Distribute the number 5 across the expression inside the parentheses:
3x+5(x+4)=0 3x + 5(x + 4) = 0 becomes 3x+5x+20=0 3x + 5x + 20 = 0 .

Step 2: Combine the like terms:
Combine 3x 3x and 5x 5x to get 8x 8x .
Thus, the equation becomes 8x+20=0 8x + 20 = 0 .

Step 3: Solve for x x :
Subtract 20 from both sides: 8x=20 8x = -20 .
Finally, divide both sides by 8: x=208 x = \frac{-20}{8} .

Simplify the fraction: x=2.5 x = -2.5 .

Therefore, the solution to the equation is x=2.5 x = -2.5 .

3

Final Answer

x=2.5 x=-2.5

Key Points to Remember

Essential concepts to master this topic
  • Distribution: Apply 5 to both terms inside parentheses first
  • Technique: Combine like terms 3x + 5x = 8x before solving
  • Check: Substitute x = -2.5: 3(-2.5) + 5(-2.5 + 4) = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute to all terms
    Don't multiply 5 by only x and forget the +4 = wrong equation! This skips a crucial step and leads to completely wrong answers. Always distribute the outside number to every single 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?

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You must distribute first because you can't combine terms that are separated by parentheses! Think of 5(x + 4) as a single unit that needs to be broken down before you can work with individual terms.

How do I know which terms are like terms?

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Like terms have the same variable with the same power. In this problem, 3x and 5x are like terms because they both have just 'x'. The number 20 stands alone as a constant.

What if I get a negative answer?

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Negative answers are completely normal in algebra! Don't second-guess yourself. Just make sure you check your work by substituting back into the original equation.

Can I solve this without distributing?

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While there might be other approaches, distributing is the most reliable method for this type of problem. It breaks down the equation into simpler parts that are easier to work with.

Why is my answer x=52 x = -\frac{5}{2} instead of -2.5?

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Both are correct! 52=2.5 -\frac{5}{2} = -2.5 because 52=2.5 \frac{5}{2} = 2.5 . You can express your answer as either a fraction or a decimal - just be consistent with what your teacher prefers.

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