Solve Linear Equation: 2(x-4)+6(x+2)=-18 Step-by-Step

Q: Why do I need to use the distributive property first?

The distributive property removes parentheses so you can see all terms clearly. Without it, you can't combine like terms properly and will get stuck!

Q: How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $ -\frac{22}{8} = -\frac{11}{4} $. Since 11 ÷ 4 = 2 remainder 3, this becomes $ -2\frac{3}{4} $.

Q: What if I get confused combining the constant terms?

Remember: addition and subtraction with integers! $ -8 + 12 = +4 $ because you have 8 negative and 12 positive, leaving 4 positive.

Q: Can I solve this without using the distributive property?

No! You must eliminate the parentheses first. There's no way to combine like terms or isolate the variable while the terms are still grouped in parentheses.

Q: How do I know if my final answer is simplified correctly?

Check if the fraction can be reduced further. $ \frac{22}{8} $ reduces to $ \frac{11}{4} $ because both 22 and 8 are divisible by 2. Always simplify to lowest terms!

Linear Equations with Mixed Number Solutions

$2(x-4)+6(x+2)=-18$

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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

00:09 Collect terms

00:17 Arrange the equation so that only the unknown X is on one side

00:24 Collect terms

00:27 Isolate X

00:37 Break down the fraction into a whole number and remainder

00:42 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

$2(x-4)+6(x+2)=-18$

Step-by-step solution

To solve the problem $2(x-4)+6(x+2)=-18$ , we follow these steps:

Step 1: Apply the distributive property.

Expand both terms using the distributive property:

$2(x-4)$ expands to $2x - 8$ and $6(x+2)$ expands to $6x + 12$ .

Thus, the equation becomes:

2x - 8 + 6x + 12 = -18

Step 2: Combine like terms.

Combine $2x$ and $6x$ to get $8x$ , and combine $-8$ and $12$ to get $4$ .

The equation simplifies to:

8x + 4 = -18

Step 3: Isolate the variable $x$ .

Subtract $4$ from both sides to isolate terms with $x$ :

8x = -18 - 4

Simplifying the right side gives:

8x = -22

Step 4: Solve for $x$ .

Divide both sides by $8$ to solve for $x$ :

x = \frac{-22}{8}

Simplify $\frac{-22}{8}$ to $-\frac{11}{4}$ , which is $-2\frac{3}{4}$ in mixed number form.

Therefore, the solution to the equation is $x = -2\frac{3}{4}$ .

Final Answer

$-2\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Expand parentheses first before combining like terms
Technique: Combine $2x + 6x = 8x$ and $-8 + 12 = 4$
Check: Substitute $x = -2\frac{3}{4}$ back: both sides equal $-18$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to both terms inside parentheses
Don't just multiply the first term like 2(x-4) = 2x - 4, ignoring the -4! This gives 2x + 6x + 12 = -18 instead of the correct 2x - 8 + 6x + 12 = -18. Always distribute to every 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 use the distributive property first?

The distributive property removes parentheses so you can see all terms clearly. Without it, you can't combine like terms properly and will get stuck!

How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $-\frac{22}{8} = -\frac{11}{4}$ . Since 11 ÷ 4 = 2 remainder 3, this becomes $-2\frac{3}{4}$ .

What if I get confused combining the constant terms?

Remember: addition and subtraction with integers! $-8 + 12 = +4$ because you have 8 negative and 12 positive, leaving 4 positive.

Can I solve this without using the distributive property?

No! You must eliminate the parentheses first. There's no way to combine like terms or isolate the variable while the terms are still grouped in parentheses.

How do I know if my final answer is simplified correctly?

Check if the fraction can be reduced further. $\frac{22}{8}$ reduces to $\frac{11}{4}$ because both 22 and 8 are divisible by 2. Always simplify to lowest terms!

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