Solve the Fraction Equation: Finding X in 1/3x + 5/6 = -1/6

Q: Why do I subtract 5/6 from both sides instead of adding?

To isolate the variable term $ \frac{1}{3}x $, we need to move $ \frac{5}{6} $ to the other side. Since it's being added to $ \frac{1}{3}x $, we subtract it from both sides.

Q: How do I subtract fractions with the same denominator?

When fractions have the same denominator, just subtract the numerators: $ -\frac{1}{6} - \frac{5}{6} = \frac{-1-5}{6} = -\frac{6}{6} = -1 $

Q: What does it mean to multiply both sides by 3?

When we have $ \frac{1}{3}x = -1 $, multiplying both sides by 3 eliminates the fraction: $ 3 \cdot \frac{1}{3}x = 3 \cdot (-1) $, which gives us $ x = -3 $

Q: Can I solve this by finding a common denominator first?

You could, but it's more efficient to isolate the variable term first. However, if you prefer, you can multiply everything by 6 (the LCD) at the start: $ 2x + 5 = -1 $

Linear Equations with Negative Fractional Solutions

Find the value of the parameter X

$\frac{1}{3}x+\frac{5}{6}=-\frac{1}{6}$

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Step-by-step video solution

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00:00 Solve the following expression

00:03 We want to isolate the unknown X

00:07 Arrange the equation with the unknown X on one side

00:19 Simplify

00:34 Multiply by the denominator in order to eliminate the fraction

00:44 Simplify further

00:50 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the value of the parameter X

$\frac{1}{3}x+\frac{5}{6}=-\frac{1}{6}$

Step-by-step solution

First, we will arrange the equation so that we have variables on one side and numbers on the other side.

Therefore, we will move $\frac{5}{6}$ to the other side, and we will get

$\frac{1}{3}x=-\frac{1}{6}-\frac{5}{6}$

Note that the two fractions on the right side share the same denominator, so you can subtract them:

$\frac{1}{3}x=-\frac{6}{6}$

Observe the minus sign on the right side!

$\frac{1}{3}x=-1$

Now, we will try to get rid of the denominator, we will do this by multiplying the entire exercise by the denominator (that is, all terms on both sides of the equation):

$1x=-3$

$x=-3$

Final Answer

-3

Key Points to Remember

Essential concepts to master this topic

Strategy: Isolate the variable term before clearing the denominator
Technique: Subtract $\frac{5}{6}$ from both sides: $-\frac{1}{6} - \frac{5}{6} = -\frac{6}{6}$
Check: Substitute x = -3: $\frac{1}{3}(-3) + \frac{5}{6} = -1 + \frac{5}{6} = -\frac{1}{6}$ ✓

Common Mistakes

Avoid these frequent errors

Sign errors when subtracting fractions
Don't forget the negative sign when combining $-\frac{1}{6} - \frac{5}{6}$ = getting $\frac{4}{6}$ instead of $-\frac{6}{6}$ ! This leads to x = 2 instead of x = -3. Always pay careful attention to negative signs when adding or subtracting fractions.

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 5/6 from both sides instead of adding?

To isolate the variable term $\frac{1}{3}x$ , we need to move $\frac{5}{6}$ to the other side. Since it's being added to $\frac{1}{3}x$ , we subtract it from both sides.

How do I subtract fractions with the same denominator?

When fractions have the same denominator, just subtract the numerators: $-\frac{1}{6} - \frac{5}{6} = \frac{-1-5}{6} = -\frac{6}{6} = -1$

What does it mean to multiply both sides by 3?

When we have $\frac{1}{3}x = -1$ , multiplying both sides by 3 eliminates the fraction: $3 \cdot \frac{1}{3}x = 3 \cdot (-1)$ , which gives us $x = -3$

Why is the answer negative?

The answer x = -3 is negative because when we combined the fractions on the right side, we got $-\frac{6}{6} = -1$ . Negative results are completely normal in algebra!

Can I solve this by finding a common denominator first?

You could, but it's more efficient to isolate the variable term first. However, if you prefer, you can multiply everything by 6 (the LCD) at the start: $2x + 5 = -1$

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