Algebra Examples

$3 - \frac{4 x}{5} = \frac{4 + x}{5}$

Step 1

Multiply both sides by $5$ .

$(3 - \frac{4 x}{5}) \cdot 5 = \frac{4 + x}{5} \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(3 - \frac{4 x}{5}) \cdot 5$ .

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Step 2.1.1.1

Apply the distributive property.

$3 \cdot 5 - \frac{4 x}{5} \cdot 5 = \frac{4 + x}{5} \cdot 5$

Step 2.1.1.2

Multiply $3$ by $5$ .

$15 - \frac{4 x}{5} \cdot 5 = \frac{4 + x}{5} \cdot 5$

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{4 x}{5}$ into the numerator.

$15 + \frac{- 4 x}{5} \cdot 5 = \frac{4 + x}{5} \cdot 5$

Step 2.1.1.3.2

Cancel the common factor.

$15 + \frac{- 4 x}{5} \cdot 5 = \frac{4 + x}{5} \cdot 5$

Step 2.1.1.3.3

Rewrite the expression.

$15 - 4 x = \frac{4 + x}{5} \cdot 5$

Step 2.1.1.4

Reorder $15$ and $- 4 x$ .

$- 4 x + 15 = \frac{4 + x}{5} \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{4 + x}{5} \cdot 5$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Cancel the common factor.

$- 4 x + 15 = \frac{4 + x}{5} \cdot 5$

Step 2.2.1.1.2

Rewrite the expression.

$- 4 x + 15 = 4 + x$

Step 2.2.1.2

Reorder $4$ and $x$ .

$- 4 x + 15 = x + 4$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$- 4 x + 15 - x = 4$

Step 3.1.2

Subtract $x$ from $- 4 x$ .

$- 5 x + 15 = 4$

Step 3.2

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

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Step 3.2.1

Subtract $15$ from both sides of the equation.

$- 5 x = 4 - 15$

Step 3.2.2

Subtract $15$ from $4$ .

$- 5 x = - 11$

Step 3.3

Divide each term in $- 5 x = - 11$ by $- 5$ and simplify.

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Step 3.3.1

Divide each term in $- 5 x = - 11$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 11}{- 5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 11}{- 5}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 11}{- 5}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{11}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{5}$

Decimal Form:

$x = 2.2$

Mixed Number Form:

$x = 2 \frac{1}{5}$