Solve the Linear Equation: 2(x+4)+8=0 Step by Step

Q: Why do I need to distribute first instead of just moving terms around?

The parentheses create a group that must be expanded first. You can't move individual terms inside parentheses until you've distributed the coefficient to each term.

Q: What's the difference between 2(x+4) and 2x+4?

$ 2(x+4) = 2x + 8 $ because you multiply both x and 4 by 2. But $ 2x + 4 $ means only the x is multiplied by 2. Big difference!

Q: How do I know when I've distributed correctly?

Count your terms! $ 2(x+4) $ should become two terms: $ 2x + 8 $. If you only have one term, you forgot to distribute to something!

Q: Why does my answer come out different when I don't distribute properly?

Because you're solving a different equation! If you write $ 2x + 4 + 8 = 0 $ instead of $ 2x + 8 + 8 = 0 $, you get $ x = -6 $ instead of the correct $ x = -8 $.

Linear Equations with Distributive Property

Determine the value of $x$ :

$2(x+4)+8=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 Open parentheses properly, multiply by each factor

00:13 Collect terms

00:22 Arrange the equation so that one side has only the unknown X

00:28 Isolate X

00:38 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

Determine the value of $x$ :

$2(x+4)+8=0$

Step-by-step solution

Let's first expand the parentheses using the formula:

$a(x+b)=ax+ab$

$(2\times x)+(2\times4)+8=0$

$2x+8+8=0$

Next, we will substitute in our terms accordingly:

$2x+16=0$

Then, we will move the 16 to the left-hand side, keeping the appropriate sign:

$2x=-16$

Finally, we divide both sides by 2:

$\frac{2x}{2}=-\frac{16}{2}$

$x=-8$

Final Answer

$x=-8$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Multiply each term inside parentheses by outside coefficient
Technique: $2(x+4) = 2x + 8$ before combining like terms
Check: Substitute $x = -8$ : $2(-8+4)+8 = -8+8 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't multiply only the first term: 2(x+4) ≠ 2x+4 = wrong answer! This ignores the second term and gives x = -6 instead of x = -8. Always multiply the outside number by every term inside the parentheses.

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 first instead of just moving terms around?

The parentheses create a group that must be expanded first. You can't move individual terms inside parentheses until you've distributed the coefficient to each term.

What's the difference between 2(x+4) and 2x+4?

$2(x+4) = 2x + 8$ because you multiply both x and 4 by 2. But $2x + 4$ means only the x is multiplied by 2. Big difference!

Can I solve this equation without distributing?

Not easily! You could divide both sides by 2 first, but that creates fractions. Distributing first keeps everything as whole numbers and makes the algebra cleaner.

How do I know when I've distributed correctly?

Count your terms! $2(x+4)$ should become two terms: $2x + 8$ . If you only have one term, you forgot to distribute to something!

Why does my answer come out different when I don't distribute properly?

Because you're solving a different equation! If you write $2x + 4 + 8 = 0$ instead of $2x + 8 + 8 = 0$ , you get $x = -6$ instead of the correct $x = -8$ .

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