Solve the Linear Equation: 7(x-4)=(6-x)×3 Step by Step

Q: Why do I need to distribute before combining like terms?

You must eliminate all parentheses first using the distributive property. You can't combine terms that are inside and outside parentheses - they're not truly like terms until the parentheses are gone!

Q: What if I get confused about which terms to move where?

Remember the goal: get all x-terms on one side and all numbers on the other side. It doesn't matter which side you choose - just be consistent and move entire terms (with their signs).

Q: How do I know if 4.6 is really the right answer?

Substitute back into the original equation: $ 7(4.6-4) = 7(0.6) = 4.2 $ and $ (6-4.6) \times 3 = 1.4 \times 3 = 4.2 $. Both sides equal 4.2, so it's correct!

Q: Can I work with decimals throughout the problem?

Absolutely! Decimals are just another way to write numbers. The same algebraic rules apply. Just be careful with your arithmetic and double-check your calculations.

Q: What if I move terms to the wrong side?

No problem! As long as you move complete terms and keep the equation balanced, you'll get the same answer. You might end up with $ -10x = -46 $, which still gives $ x = 4.6 $.

Linear Equations with Distributive Property

Solve for X:

$7(x-4)=(6-x)\times3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 Make sure to open parentheses properly, multiply by each factor

00:21 Solve each multiplication separately

00:27 Positive times negative is always negative

00:51 Arrange the equation so that X is isolated on one side

01:14 Collect like terms

01:25 Isolate X

01:33 Simplify as much as possible

01:38 And that's the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$7(x-4)=(6-x)\times3$

Step-by-step solution

The goal is to solve the linear equation $7(x-4) = (6-x) \times 3$ . Follow these steps to find the solution:

Step 1: Open the parentheses using the distributive property. This gives us: $7(x - 4) = 7x - 28$ $(6 - x) \times 3 = 18 - 3x$ Thus, the equation becomes: $7x - 28 = 18 - 3x$
Step 2: Combine like terms by getting all $x$ -terms on one side and constant terms on the other. $7x + 3x = 18 + 28$ Simplify to get: $10x = 46$
Step 3: Solve for $x$ by dividing both sides by 10. $x = \frac{46}{10} = 4.6$

Therefore, the solution to the problem is $x = 4.6$ .

Final Answer

$4.6$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply each term inside parentheses by outside coefficient
Technique: Move all x-terms to one side: $7x + 3x = 10x$
Check: Substitute x = 4.6: $7(0.6) = 3(1.4) = 4.2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms in parentheses
Don't multiply 7(x-4) and get just 7x = wrong answer! This ignores the -4 term completely. Always distribute to every single term: 7(x-4) = 7x - 28.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ x - 3 + 5 = 8 - 2 $$

FAQ

Everything you need to know about this question

Why do I need to distribute before combining like terms?

You must eliminate all parentheses first using the distributive property. You can't combine terms that are inside and outside parentheses - they're not truly like terms until the parentheses are gone!

What if I get confused about which terms to move where?

Remember the goal: get all x-terms on one side and all numbers on the other side. It doesn't matter which side you choose - just be consistent and move entire terms (with their signs).

How do I know if 4.6 is really the right answer?

Substitute back into the original equation: $7(4.6-4) = 7(0.6) = 4.2$ and $(6-4.6) \times 3 = 1.4 \times 3 = 4.2$ . Both sides equal 4.2, so it's correct!

Can I work with decimals throughout the problem?

Absolutely! Decimals are just another way to write numbers. The same algebraic rules apply. Just be careful with your arithmetic and double-check your calculations.

What if I move terms to the wrong side?

No problem! As long as you move complete terms and keep the equation balanced, you'll get the same answer. You might end up with $-10x = -46$ , which still gives $x = 4.6$ .

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Solve the Linear Equation: 7(x-4)=(6-x)×3 Step by Step

Linear Equations with Distributive Property

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to distribute before combining like terms?

What if I get confused about which terms to move where?

How do I know if 4.6 is really the right answer?

Can I work with decimals throughout the problem?

What if I move terms to the wrong side?

🌟 Unlock Your Math Potential

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