Solve Linear Equation: -6(7x-6)-(-5-8x)=0 Step by Step

Q: Why do I get confused with all these negative signs?

Negative signs can be tricky! Remember: when you have two negatives together like $ -(-5) $, they become positive. Think of it as "the opposite of the opposite brings you back to positive."

Q: How do I distribute a negative number correctly?

When distributing a negative like $ -6(7x-6) $, multiply the -6 by each term inside: $ (-6)(7x) + (-6)(-6) = -42x + 36 $. The key is keeping track of positive and negative products!

Q: What's the difference between -(-5-8x) and -(5+8x)?

Great question! $ -(-5-8x) $ means "the opposite of negative 5 minus 8x" which becomes $ +5 + 8x $. But $ -(5+8x) $ means "the opposite of 5 plus 8x" which becomes $ -5 - 8x $.

Q: Why is my final answer a mixed number?

Mixed numbers like $ 1\frac{7}{34} $ are just another way to write improper fractions! Since $ \frac{41}{34} = 1 + \frac{7}{34} $, both forms are correct. Choose whichever format your teacher prefers.

Q: How can I double-check my algebra steps?

After each step, ask yourself: "Did I do the same thing to both sides?" Also, substitute your final answer back into the original equation. If you get 0 = 0, you're right!

Linear Equations with Negative Distributive Property

$-6(7x-6)-(-5-8x)=0$

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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

00:06 Negative times negative always equals positive

00:16 Collect terms

00:28 Arrange the equation so that only the unknown X is on one side

00:35 Isolate X

00:41 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

$-6(7x-6)-(-5-8x)=0$

Step-by-step solution

We will use the extended division rule and the formula:

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

$-42x+36+5+8x=0$

Let's input the appropriate terms:

$-34x+41=0$

We'll move -34x to the right side and maintain the appropriate sign:

$41=34x$

Let's divide both sides by 34:

$\frac{41}{34}=\frac{34x}{34}$

$\frac{41}{34}=x$

We'll convert the simple fraction to a mixed fraction:

$x=1\frac{7}{34}$

Final Answer

$1\frac{7}{34}$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply negative signs carefully when distributing across parentheses
Technique: $-6(7x-6) = -42x + 36$ and $-(-5-8x) = 5 + 8x$
Check: Substitute $x = 1\frac{7}{34}$ back: $-34(\frac{41}{34}) + 41 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly handling double negatives when distributing
Don't distribute $-(-5-8x)$ as $-5-8x$ = wrong signs! The negative outside flips both signs inside. Always remember: negative times negative equals positive, so $-(-5-8x) = +5 + 8x$ .

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do I get confused with all these negative signs?

Negative signs can be tricky! Remember: when you have two negatives together like $-(-5)$ , they become positive. Think of it as "the opposite of the opposite brings you back to positive."

How do I distribute a negative number correctly?

When distributing a negative like $-6(7x-6)$ , multiply the -6 by each term inside: $(-6)(7x) + (-6)(-6) = -42x + 36$ . The key is keeping track of positive and negative products!

What's the difference between -(-5-8x) and -(5+8x)?

Great question! $-(-5-8x)$ means "the opposite of negative 5 minus 8x" which becomes $+5 + 8x$ . But $-(5+8x)$ means "the opposite of 5 plus 8x" which becomes $-5 - 8x$ .

Why is my final answer a mixed number?

Mixed numbers like $1\frac{7}{34}$ are just another way to write improper fractions! Since $\frac{41}{34} = 1 + \frac{7}{34}$ , both forms are correct. Choose whichever format your teacher prefers.

How can I double-check my algebra steps?

After each step, ask yourself: "Did I do the same thing to both sides?" Also, substitute your final answer back into the original equation. If you get 0 = 0, you're right!

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