Solve for X in the Linear Equation: 6-4x=-18

Q: What happens when I divide two negative numbers?

When you divide two negative numbers, the result is positive! So $ \frac{-24}{-4} = 6 $. Remember: negative ÷ negative = positive.

Q: How can x be positive when the equation has -4x?

The coefficient -4 doesn't determine the sign of x! Since $ -4x = -24 $, we need a positive value of x to make the left side negative.

Q: Can I add 4x to both sides instead?

You could, but it's harder! You'd get $ 6 = -18 + 4x $, then $ 24 = 4x $. The standard approach of moving constants first is simpler and less error-prone.

Q: How do I check if x = 6 is correct?

Substitute x = 6 into the original equation: $ 6 - 4(6) = 6 - 24 = -18 $. Since this equals -18, our answer is correct!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Alright, let's solve this problem.

00:09 First, we need to focus on getting X alone.

00:13 Let's rearrange the equation so that only X is on one side.

00:25 Now, we'll simplify everything we can.

00:35 Next, let's isolate X and find its value.

00:51 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve for X:

$6-4x=-18$

2

Step-by-step solution

To solve the equation $6 - 4x = -18$ , we follow these steps:

Step 1: Subtract 6 from both sides of the equation to begin isolating the term with $x$ :

$6 - 4x - 6 = -18 - 6$

This simplifies to:

$-4x = -24$

Step 2: Divide both sides by -4 to solve for $x$ :

$\frac{-4x}{-4} = \frac{-24}{-4}$

The equation simplifies to:

$x = 6$

Thus, the solution to the equation is $x = 6$ .

3

Final Answer

6

Key Points to Remember

Essential concepts to master this topic

Rule: Move constant terms first, then divide by coefficient
Technique: Subtract 6 from both sides: $-4x = -24$
Check: Substitute back: $6 - 4(6) = 6 - 24 = -18$ ✓

Common Mistakes

Avoid these frequent errors

Adding 4x to both sides instead of subtracting 6
Don't add 4x to both sides first = $6 = -18 + 4x$ ! This creates unnecessary complexity with negative coefficients. Always isolate the variable term by moving constants first, then divide.

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 subtract 6 from both sides first?

+

Subtracting 6 removes the constant from the left side, leaving just the variable term $-4x$ . This makes it easier to see that we need to divide by -4 to solve for x.

What happens when I divide two negative numbers?

+

When you divide two negative numbers, the result is positive! So $\frac{-24}{-4} = 6$ . Remember: negative ÷ negative = positive.

How can x be positive when the equation has -4x?

+

The coefficient -4 doesn't determine the sign of x! Since $-4x = -24$ , we need a positive value of x to make the left side negative.

Can I add 4x to both sides instead?

+

You could, but it's harder! You'd get $6 = -18 + 4x$ , then $24 = 4x$ . The standard approach of moving constants first is simpler and less error-prone.

How do I check if x = 6 is correct?

+

Substitute x = 6 into the original equation: $6 - 4(6) = 6 - 24 = -18$ . Since this equals -18, our answer is correct!

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Solve for X in the Linear Equation: 6-4x=-18

Linear Equations with Negative Constants

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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 subtract 6 from both sides first?

What happens when I divide two negative numbers?

How can x be positive when the equation has -4x?

Can I add 4x to both sides instead?

How do I check if x = 6 is correct?

🌟 Unlock Your Math Potential

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