Solve for X: -8+x-3(x-2)=5(2+x)-4+3x Linear Equation

Q: Why did -3 times -2 become +6?

When you distribute -3(x-2), you multiply -3 by each term inside. Since negative times negative equals positive, (-3) × (-2) = +6!

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

Like terms have the same variable with the same power. In this problem, x terms (-3x, +x, +5x, +3x) combine together, and constants (-8, +6, +10, -4) combine together.

Q: Can I simplify -8/10 further?

Yes! $ -\frac{8}{10} = -\frac{4}{5} $ when you divide both numerator and denominator by their greatest common factor of 2.

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

No problem! Just remember to change the sign when moving terms across the equals sign. Moving +8x to the left becomes -8x, and moving -2 to the right becomes +2.

Q: How can I check if my distribution was correct?

Left side: -3(x-2) should become -3x + 6Right side: 5(2+x) should become 10 + 5xDouble-check that you didn't miss any terms when combining!

Linear Equations with Distribution and Combining Terms

Solve for x:

$-8+x-3(x-2)=5(2+x)-4+3x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:05 Open parentheses properly, multiply by each factor

00:28 Collect like terms

00:55 Arrange the equation so that X is isolated on one side

01:12 Collect like terms

01:16 Isolate X

01:22 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:

$-8+x-3(x-2)=5(2+x)-4+3x$

Step-by-step solution

First, we will expand the parentheses on both sides by multiplying their contents by the number outside:

$-8+x-3\times x+(-3)\times(-2)=5\times2+5\times x-4+3x$

$-8+x-3x+6=10+5x-4+3x$

Now we collect like terms on both sides:

$-2-2x=6+8x$

We move 8x to the left and -2 to the right side, remembering to leave the plus and minus signs unchanged accordingly:

$-2x-8x=6+2$

We add the terms together:

$-10x=8$

Finally, we divide both sides by negative 10:

$\frac{-10x}{-10}=\frac{8}{-10}$

$x=-\frac{8}{10}$

Final Answer

$-\frac{8}{10}$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Multiply each term inside parentheses by the outside number
Technique: Collect like terms: -3x and +x combine to -2x
Check: Substitute $x = -\frac{8}{10}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Incorrectly distributing negative signs
Don't forget to change signs when distributing negatives like -3(x-2) = -3x + 6! Students often write -3x - 6 instead, getting the wrong final answer. Always remember that negative times negative equals positive.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why did -3 times -2 become +6?

When you distribute -3(x-2), you multiply -3 by each term inside. Since negative times negative equals positive, (-3) × (-2) = +6!

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

Like terms have the same variable with the same power. In this problem, x terms (-3x, +x, +5x, +3x) combine together, and constants (-8, +6, +10, -4) combine together.

Can I simplify -8/10 further?

Yes! $-\frac{8}{10} = -\frac{4}{5}$ when you divide both numerator and denominator by their greatest common factor of 2.

What if I move terms to the wrong side?

No problem! Just remember to change the sign when moving terms across the equals sign. Moving +8x to the left becomes -8x, and moving -2 to the right becomes +2.

How can I check if my distribution was correct?

Left side: -3(x-2) should become -3x + 6
Right side: 5(2+x) should become 10 + 5x
Double-check that you didn't miss any terms when combining!

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