Solve for X in the Equation: 8+2(x+1)=7x Using Distribution

Q: Why do I need to distribute first instead of solving differently?

The distributive property is required when you have a number multiplied by parentheses. You must eliminate the parentheses before combining like terms, otherwise you'll get the wrong answer.

Q: What if I move terms around before distributing?

Don't do this! You need to distribute first to properly expand the expression. Moving terms with undistributed parentheses will lead to errors in your calculations.

Q: How do I know which terms are 'like terms'?

Like terms have the same variable with the same exponent. In this problem, $ 2x $ and $ 7x $ are like terms, while $ 8 $ and $ 2 $ are constant terms.

Q: Can I check my answer a different way?

Yes! Substitute $ x = 2 $ into the original equation: $ 8 + 2(2 + 1) = 8 + 2(3) = 8 + 6 = 14 $ and $ 7(2) = 14 $. Both sides equal 14, so the answer is correct!

Linear Equations with Distribution Property

Solve for X:

$8+2(x+1)=7x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this equation together.

00:10 Our goal is to find the value of X.

00:13 First, open the parentheses carefully and multiply each term inside.

00:25 Remember to calculate each multiplication separately.

00:36 Next, let's combine like terms.

00:43 Now, we need to isolate X by itself.

00:58 Simplify any parts if possible.

01:04 Continue to isolate X to find its value.

01:12 And that's the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$8+2(x+1)=7x$

Step-by-step solution

To solve the given equation $8 + 2(x + 1) = 7x$ , we'll follow these steps:

Step 1: Distribute the $2$ inside the parentheses.
Step 2: Combine like terms and simplify both sides.
Step 3: Isolate the variable $x$ on one side of the equation.

Now, let's apply these steps:
Step 1: Distribute the $2$ in the equation: $2(x + 1) = 2x + 2$ Therefore, the equation becomes: $8 + 2x + 2 = 7x$ Step 2: Combine like terms on the left side: $10 + 2x = 7x$ Step 3: Isolate $x$ by moving all terms involving $x$ to one side and constants to the other: $10 = 7x - 2x$ $10 = 5x$ To solve for $x$ , divide both sides by $5$ : $x = \frac{10}{5} = 2$

Therefore, the solution to the equation is $x = 2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Multiply term outside parentheses by each term inside
Technique: $2(x + 1) = 2x + 2$ before combining like terms
Check: Substitute $x = 2$ : $8 + 2(3) = 14 = 7(2)$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't just multiply 2 × x and forget the +1 = wrong equation! This gives $8 + 2x + 1 = 7x$ instead of $8 + 2x + 2 = 7x$ , leading to x = 1 instead of x = 2. Always distribute to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to distribute first instead of solving differently?

The distributive property is required when you have a number multiplied by parentheses. You must eliminate the parentheses before combining like terms, otherwise you'll get the wrong answer.

What if I move terms around before distributing?

Don't do this! You need to distribute first to properly expand the expression. Moving terms with undistributed parentheses will lead to errors in your calculations.

How do I know which terms are 'like terms'?

Like terms have the same variable with the same exponent. In this problem, $2x$ and $7x$ are like terms, while $8$ and $2$ are constant terms.

Can I check my answer a different way?

Yes! Substitute $x = 2$ into the original equation: $8 + 2(2 + 1) = 8 + 2(3) = 8 + 6 = 14$ and $7(2) = 14$ . Both sides equal 14, so the answer is correct!

What if I get a different answer when I check?

If your check doesn't work, you made an error somewhere! Go back and carefully check your distribution step and combining like terms. These are the most common places for mistakes.

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