Solve for X in the Equation 6x = -12.6: Linear Equation Practice

Q: Why do I divide by 6 instead of subtract 6?

Because 6 is multiplied by x, not added! To undo multiplication, you must use the opposite operation - division. Think: 6 × x = -12.6, so x = -12.6 ÷ 6.

Q: How do I divide a negative number by a positive number?

When dividing negative by positive, the result is always negative! So $ \frac{-12.6}{6} = -2.1 $. Remember: different signs = negative result.

Q: Can I check my answer without substituting back?

Substitution is the best way to verify! Calculate $ 6 \times (-2.1) $ and see if you get -12.6. This confirms your solution is correct.

Linear Equations with Decimal Division

$6x=-12.6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 We divide by the coefficient of the unknown to isolate X

00:11 We divide the fraction into a whole number and remainder

00:19 We convert from improper fraction to whole number

00:22 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

$6x=-12.6$

Step-by-step solution

To solve the equation $6x = -12.6$ , we need to isolate $x$ . We achieve this by performing the following steps:

Step 1: Identify the coefficient of $x$ , which is $6$ . We aim to isolate $x$ by dividing both sides of the equation by $6$ .
Step 2: Divide both sides of the equation by $6$ to solve for $x$ . This will eliminate the coefficient and reveal the value of $x$ .

Let's perform these calculations:

$\frac{6x}{6} = \frac{-12.6}{6}$

Simplifying both sides gives:

$x = -2.1$

Therefore, the solution to the equation is $\boldsymbol{x = -2.1}$ .

Final Answer

$x=-2.1$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both sides by coefficient to isolate variable
Technique: Calculate $\frac{-12.6}{6} = -2.1$ by division
Check: Substitute back: $6(-2.1) = -12.6$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting instead of dividing by coefficient
Don't add or subtract 6 from both sides when solving $6x = -12.6$ = wrong operation! This doesn't isolate x and leads to completely incorrect answers. Always divide both sides by the coefficient of x.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I divide by 6 instead of subtract 6?

Because 6 is multiplied by x, not added! To undo multiplication, you must use the opposite operation - division. Think: 6 × x = -12.6, so x = -12.6 ÷ 6.

How do I divide a negative number by a positive number?

When dividing negative by positive, the result is always negative! So $\frac{-12.6}{6} = -2.1$ . Remember: different signs = negative result.

What if I get a decimal answer instead of a whole number?

Decimal answers are completely normal! Many linear equations have decimal solutions. Just make sure your decimal calculation is accurate and always verify your answer.

Can I check my answer without substituting back?

Substitution is the best way to verify! Calculate $6 \times (-2.1)$ and see if you get -12.6. This confirms your solution is correct.

What if I made an arithmetic error in my division?

Double-check by doing the division again or use a calculator! Common errors include sign mistakes or decimal placement. If your check doesn't work, recalculate the division step.

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