Simplify and Solve: Finding X in 8(x+3) - 1 + 4x = 8(x+3) - 5(x-4)

Q: Why do I get the same term 8(x+3) on both sides?

That's actually helpful! Since 8(x+3) appears on both sides, you can subtract it from both sides to eliminate it completely, making the equation simpler to solve.

Q: How do I handle the fraction 7/3 as my answer?

The fraction $ \frac{7}{3} $ is already in simplest form since 7 and 3 share no common factors. You can leave it as an improper fraction or write it as $ 2\frac{1}{3} $.

Q: What if I make a sign error with -5(x-4)?

Be careful with distribution! Remember that -5(x-4) = -5x + 20, not -5x - 20. The negative sign outside changes both terms inside.

Q: Can I solve this without expanding everything first?

You could try, but it's much easier to expand first! This way you can see all like terms clearly and combine them systematically without missing anything.

Q: How do I check if 7/3 is really correct?

Substitute $ x = \frac{7}{3} $ into the original equation. Calculate both sides separately - if they equal the same value, your answer is correct!

Linear Equations with Fractional Solutions

Solve for X:

$8(x+3)-1+4x=8(x+3)-5(x-4)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Subtract the common term to simplify

00:21 Open brackets properly, multiply by each factor

00:33 Arrange the equation so that one side has only the unknown X

00:49 Group like terms

00:57 Isolate X

01:02 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:

$8(x+3)-1+4x=8(x+3)-5(x-4)$

Step-by-step solution

To solve for $x$ in the equation $8(x+3)-1+4x=8(x+3)-5(x-4)$ , follow these steps:

Step 1: Expand the expressions on both sides of the equation.
Open up the terms: $8(x + 3)$ becomes $8x + 24$ , and $5(x - 4)$ becomes $5x - 20$ .
Step 2: Simplify each side.
Starting with the left-hand side:
$8(x + 3) - 1 + 4x$ simplifies to $8x + 24 - 1 + 4x = 12x + 23$ .
For the right-hand side:
$8(x + 3) - 5(x - 4)$ simplifies to $8x + 24 - 5x + 20 = 3x + 44$ .
Step 3: Set the simplified expressions equal and solve for $x$ .
This gives you the equation: $12x + 23 = 3x + 44$ .
Step 4: Isolate $x$ .
Subtract $3x$ from both sides:
$12x - 3x + 23 = 44$ simplifies to $9x + 23 = 44$ .
Subtract 23 from both sides to isolate the term with $x$ :
$9x = 21$ .
Step 5: Solve for $x$ .
Divide both sides by 9:
$x = \frac{21}{9} = \frac{7}{3}$ .

Therefore, the solution to the equation is $x = \frac{7}{3}$ .

Final Answer

$\frac{7}{3}$

Key Points to Remember

Essential concepts to master this topic

Distribution: Expand parentheses first: 8(x+3) becomes 8x + 24
Technique: Combine like terms: 8x + 4x = 12x on left side
Check: Substitute $x = \frac{7}{3}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms in parentheses
Don't just multiply 8 × x and forget the +3 = missing terms! This creates an incomplete equation with wrong coefficients. Always distribute to every term inside parentheses: 8(x+3) = 8x + 24.

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 get the same term 8(x+3) on both sides?

That's actually helpful! Since 8(x+3) appears on both sides, you can subtract it from both sides to eliminate it completely, making the equation simpler to solve.

How do I handle the fraction 7/3 as my answer?

The fraction $\frac{7}{3}$ is already in simplest form since 7 and 3 share no common factors. You can leave it as an improper fraction or write it as $2\frac{1}{3}$ .

What if I make a sign error with -5(x-4)?

Be careful with distribution! Remember that -5(x-4) = -5x + 20, not -5x - 20. The negative sign outside changes both terms inside.

Can I solve this without expanding everything first?

You could try, but it's much easier to expand first! This way you can see all like terms clearly and combine them systematically without missing anything.

How do I check if 7/3 is really correct?

Substitute $x = \frac{7}{3}$ into the original equation. Calculate both sides separately - if they equal the same value, your answer is correct!

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