Pre-Algebra Examples

$4 x + \frac{5}{6} = 5 x - \frac{5}{6}$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Subtract $5 x$ from both sides of the equation.

$4 x + \frac{5}{6} - 5 x = - \frac{5}{6}$

Step 1.2

Subtract $5 x$ from $4 x$ .

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

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $\frac{5}{6}$ from both sides of the equation.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $5$ from $- 5$ .

$- x = \frac{- 10}{6}$

Step 2.4

Cancel the common factor of $- 10$ and $6$ .

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Step 2.4.1

Factor $2$ out of $- 10$ .

$- x = \frac{2 (- 5)}{6}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $6$ .

$- x = \frac{2 \cdot - 5}{2 \cdot 3}$

Step 2.4.2.2

Cancel the common factor.

$- x = \frac{2 \cdot - 5}{2 \cdot 3}$

Step 2.4.2.3

Rewrite the expression.

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

Step 2.5

Move the negative in front of the fraction.

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

Step 3

Divide each term in $- x = - \frac{5}{3}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = - \frac{5}{3}$ by $- 1$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

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

Step 3.3.2

Divide $\frac{5}{3}$ by $1$ .

$x = \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{3}$

Decimal Form:

$x = 1.\overline{6}$

Mixed Number Form:

$x = 1 \frac{2}{3}$