Solve the Linear Equation: Arrange to Find X in -5x + 3 - 8 + 4x = 3x - 5 + 10x

Q: Why do I combine like terms first before moving variables?

Combining like terms simplifies each side, making it easier to see what you're working with. If you move variables too early, you'll have more terms to track and higher chance of errors!

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

Like terms have the same variable with the same exponent. So $ -5x $ and $ 4x $ are like terms, but $ 3 $ and $ -8 $ are separate constant terms.

Q: How can I check if x = 0 is correct?

Substitute $ x = 0 $ into the original equation: $ -5(0) + 3 - 8 + 4(0) = 3(0) - 5 + 10(0) $. Both sides equal $ -5 $, so it's correct!

Q: Why did adding x to both sides eliminate the x term on the left?

Because $ -x + x = 0 $! Adding the opposite of a term cancels it out completely. This is how we isolate variables by moving them to one side.

Linear Equations with Like Term Combining

Solve for X:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 Collect like terms

00:19 Arrange the equation so that one side has only the unknown X

00:39 Collect like terms

00:46 Isolate X

00:51 And this is 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:

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

Step-by-step solution

To solve this problem, we'll follow these steps:

Simplify both sides of the equation.
Combine like terms to isolate $x$ .
Solve for $x$ by equating coefficients.

Now, let's work through each step:

Step 1: Simplify both sides
The original equation is:

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

Simplify each side by combining like terms:

Left side: $-5x + 4x + 3 - 8$ becomes $-x - 5$ .

Right side: $3x + 10x - 5$ becomes $13x - 5$ .

Now the equation is:

$-x - 5 = 13x - 5$

Step 2: Remove like terms
Add $x$ to both sides to move terms involving $x$ together:

$-5 = 14x - 5$

Step 3: Isolate the constant terms:
Add 5 to both sides:

$0 = 14x$

Step 4: Solve for $x$
Divide both sides by 14:

$x = 0$

Therefore, the solution to the problem is $x = 0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Simplify First: Combine like terms on each side before moving variables
Move Variables: Add x to both sides: -x - 5 becomes -5 = 14x - 5
Verify Solution: Substitute x = 0: both sides equal -5 ✓

Common Mistakes

Avoid these frequent errors

Moving variables before combining like terms
Don't move variables across the equals sign before simplifying each side = confusing mess with wrong coefficients! This creates unnecessary complexity and calculation errors. Always combine like terms on each side first, then move variables.

Practice Quiz

Test your knowledge with interactive questions

$$ -16+a=-17 $$

FAQ

Everything you need to know about this question

Why do I combine like terms first before moving variables?

Combining like terms simplifies each side, making it easier to see what you're working with. If you move variables too early, you'll have more terms to track and higher chance of errors!

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

Like terms have the same variable with the same exponent. So $-5x$ and $4x$ are like terms, but $3$ and $-8$ are separate constant terms.

What if I get x = 0 as my answer?

Zero is a perfectly valid solution! Don't second-guess yourself. When $x = 0$ , it means the variable term disappears, leaving only the constants to balance the equation.

How can I check if x = 0 is correct?

Substitute $x = 0$ into the original equation: $-5(0) + 3 - 8 + 4(0) = 3(0) - 5 + 10(0)$ . Both sides equal $-5$ , so it's correct!

Why did adding x to both sides eliminate the x term on the left?

Because $-x + x = 0$ ! Adding the opposite of a term cancels it out completely. This is how we isolate variables by moving them to one side.

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