Solve Linear Equation: 2x+7-5x-12=-8x+3 Step by Step

Q: Why do I need to collect like terms on the same side?

Collecting like terms simplifies the equation and makes it easier to solve. When variables are scattered on both sides, it's harder to see what coefficient x actually has.

Q: What if I get confused about which sign to use?

Remember: when you move a term across the equals sign, flip its sign! Positive becomes negative, negative becomes positive. Write each step clearly to avoid mistakes.

Q: How do I handle multiple variable terms like 2x - 5x + 8x?

Combine them step by step: 2x - 5x = -3x, then -3x + 8x = 5x. Don't try to do it all at once - work systematically!

Q: Why is my final answer a fraction instead of a whole number?

Many linear equations have fractional solutions - this is completely normal! Just make sure your fraction is in simplest form and verify by substituting back.

Q: What's the difference between moving terms and combining like terms?

Moving terms means transferring them across the equals sign (with sign change). Combining like terms means adding/subtracting terms with the same variable on the same side.

Q: How can I check if $ x = \frac{8}{5} $ is really correct?

Substitute back into the original equation: $ 2(\frac{8}{5}) + 7 - 5(\frac{8}{5}) - 12 = -8(\frac{8}{5}) + 3 $. Both sides should equal -8.

Linear Equations with Multiple Variable Terms

Solve the following problem:

$2x+7-5x-12=-8x+3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's start by solving the equation.

00:14 First, we need to collect like terms together.

00:30 Our goal is to have the unknown, X, alone on one side.

00:46 Let's collect the terms again to simplify the equation.

00:53 Now, we reduce what we can to make it simpler.

00:59 Next, we need to isolate the unknown, X.

01:21 Keep reducing until we can't anymore.

01:25 And there you go! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$2x+7-5x-12=-8x+3$

Step-by-step solution

In order to solve this exercise, we first need to identify that we have an equation with an unknown.

To solve such equations, the first step will be to arrange the equation so that on one side we have the numbers and on the other side the unknowns.

$2X+7-5X-12=-8X+3$

First, we'll move all unknowns to one side.
It's important to remember that when moving terms, the sign of the number changes (from negative to positive or vice versa).

$2X+7-5X-12+8X=3$

Now we'll do the same thing with the regular numbers.

$2X-5X+8X=3-7+12$

In the next step, we'll calculate the numbers according to the addition and subtraction signs.

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

$3-7=-4$
$-4+12=8$

$5X=8$

At this stage, we want to reach a state where we have only one $X$ , not $5X$ ,
Thus we'll divide both sides of the equation by the coefficient of the unknown (in this case - 5).

$X={8\over5}$

Final Answer

$x=\frac{8}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Collect all variable terms on one side, constants on other
Technique: Move -8x to left: 2x - 5x + 8x = 5x
Check: Substitute x = 8/5: 2(8/5) - 5(8/5) + 8(8/5) = 8 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change signs when moving terms
Don't move -8x to the left as -8x = wrong coefficient! When you move a term across the equals sign, its sign must flip. Always change -8x to +8x when moving it from right to left side.

Practice Quiz

Test your knowledge with interactive questions

Solve for $$ b $$ :

$$ 8-b=6 $$

FAQ

Everything you need to know about this question

Why do I need to collect like terms on the same side?

Collecting like terms simplifies the equation and makes it easier to solve. When variables are scattered on both sides, it's harder to see what coefficient x actually has.

What if I get confused about which sign to use?

Remember: when you move a term across the equals sign, flip its sign! Positive becomes negative, negative becomes positive. Write each step clearly to avoid mistakes.

How do I handle multiple variable terms like 2x - 5x + 8x?

Combine them step by step: 2x - 5x = -3x, then -3x + 8x = 5x. Don't try to do it all at once - work systematically!

Why is my final answer a fraction instead of a whole number?

Many linear equations have fractional solutions - this is completely normal! Just make sure your fraction is in simplest form and verify by substituting back.

What's the difference between moving terms and combining like terms?

Moving terms means transferring them across the equals sign (with sign change). Combining like terms means adding/subtracting terms with the same variable on the same side.

How can I check if $x = \frac{8}{5}$ is really correct?

Substitute back into the original equation: $2(\frac{8}{5}) + 7 - 5(\frac{8}{5}) - 12 = -8(\frac{8}{5}) + 3$ . Both sides should equal -8.

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Solve Linear Equation: 2x+7-5x-12=-8x+3 Step by Step

Linear Equations with Multiple Variable Terms

❤️ 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 collect like terms on the same side?

What if I get confused about which sign to use?

How do I handle multiple variable terms like 2x - 5x + 8x?

Why is my final answer a fraction instead of a whole number?

What's the difference between moving terms and combining like terms?

How can I check if x=85 x = \frac{8}{5} x=58​ is really correct?

🌟 Unlock Your Math Potential

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How can I check if $x = \frac{8}{5}$ is really correct?