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

Q: Why does negative divided by negative equal positive?

When you divide two negative numbers, the result is always positive! Think of it as: $ \frac{-6x}{-6} = \frac{-6 \cdot x}{-6} = x $. The negatives cancel out.

Q: What if I multiply both sides by -1/6 instead?

That works too! Multiplying by -1/6 is the same as dividing by -6. You'll get: $ (-1/6)(-6x) = (-1/6)(18) $, which gives $ x = -3 $.

Q: How do I remember which operation undoes multiplication?

Division undoes multiplication! If x is multiplied by -6, then divide by -6 to isolate x. Think of it as opposite operations that cancel each other out.

Q: Can I add 6x to both sides instead?

No, that won't work here! Adding 6x to both sides gives $ 0 = 18 + 6x $, which is more complicated. Always use division when the variable has a coefficient.

Q: What if my answer is positive instead of negative?

Double-check your division! $ \frac{18}{-6} = -3 $, not +3. When dividing a positive by a negative, the result is always negative.

Linear Equations with Negative Coefficients

$-6x=18$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve the problem.

00:06 We need to find the value of X.

00:10 First, we'll focus on isolating X.

00:21 Now, factor 18 into 6 and 3.

00:25 Next, simplify where possible.

00:29 And, that's the solution! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-6x=18$

Step-by-step solution

To solve the equation $-6x = 18$ , we need to isolate the variable $x$ .

Our equation is:

$-6x = 18$

The variable $x$ is multiplied by $-6$ . To undo this operation and solve for $x$ , we divide both sides of the equation by $-6$ . This will isolate $x$ on one side of the equation:

$\frac{-6x}{-6} = \frac{18}{-6}$

Simplifying both sides, we find:

$x = -3$

Thus, the solution to the equation $-6x = 18$ is $x = -3$ .

Therefore, the correct answer is $x = -3$ .

Final Answer

$-3$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Divide both sides by the coefficient of x
Division Technique: $\frac{-6x}{-6} = \frac{18}{-6}$ gives $x = -3$
Verification Check: Substitute back: $-6(-3) = 18$ equals $18 = 18$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to apply division to both sides of equation
Don't just divide the left side by -6 = $x = 18$ ! This violates the equality principle and gives the wrong answer. Always perform the same operation on both sides of the equation to maintain balance.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why does negative divided by negative equal positive?

When you divide two negative numbers, the result is always positive! Think of it as: $\frac{-6x}{-6} = \frac{-6 \cdot x}{-6} = x$ . The negatives cancel out.

What if I multiply both sides by -1/6 instead?

That works too! Multiplying by -1/6 is the same as dividing by -6. You'll get: $(-1/6)(-6x) = (-1/6)(18)$ , which gives $x = -3$ .

How do I remember which operation undoes multiplication?

Division undoes multiplication! If x is multiplied by -6, then divide by -6 to isolate x. Think of it as opposite operations that cancel each other out.

Can I add 6x to both sides instead?

No, that won't work here! Adding 6x to both sides gives $0 = 18 + 6x$ , which is more complicated. Always use division when the variable has a coefficient.

What if my answer is positive instead of negative?

Double-check your division! $\frac{18}{-6} = -3$ , not +3. When dividing a positive by a negative, the result is always negative.

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