Algebra Examples

$x + 1 \frac{4}{5} = \frac{4 + 5 x}{5}$

Step 1

Simplify the left side.

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Step 1.1

Convert $1 \frac{4}{5}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$x + 1 + \frac{4}{5} = \frac{4 + 5 x}{5}$

Step 1.1.2

Add $1$ and $\frac{4}{5}$ .

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Step 1.1.2.1

Write $1$ as a fraction with a common denominator.

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

Step 1.1.2.2

Combine the numerators over the common denominator.

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

Step 1.1.2.3

Add $5$ and $4$ .

$x + \frac{9}{5} = \frac{4 + 5 x}{5}$

Step 2

Multiply both sides by $5$ .

$(x + \frac{9}{5}) \cdot 5 = \frac{4 + 5 x}{5} \cdot 5$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $(x + \frac{9}{5}) \cdot 5$ .

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Step 3.1.1.1

Apply the distributive property.

$x \cdot 5 + \frac{9}{5} \cdot 5 = \frac{4 + 5 x}{5} \cdot 5$

Step 3.1.1.2

Move $5$ to the left of $x$ .

$5 \cdot x + \frac{9}{5} \cdot 5 = \frac{4 + 5 x}{5} \cdot 5$

Step 3.1.1.3

Cancel the common factor of $5$ .

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Step 3.1.1.3.1

Cancel the common factor.

$5 \cdot x + \frac{9}{5} \cdot 5 = \frac{4 + 5 x}{5} \cdot 5$

Step 3.1.1.3.2

Rewrite the expression.

$5 \cdot x + 9 = \frac{4 + 5 x}{5} \cdot 5$

$5 x + 9 = \frac{4 + 5 x}{5} \cdot 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

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Step 3.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1

Cancel the common factor.

$5 x + 9 = \frac{4 + 5 x}{5} \cdot 5$

Step 3.2.1.1.2

Rewrite the expression.

$5 x + 9 = 4 + 5 x$

Step 3.2.1.2

Reorder $4$ and $5 x$ .

$5 x + 9 = 5 x + 4$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

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

$5 x + 9 - 5 x = 4$

Step 4.1.2

Combine the opposite terms in $5 x + 9 - 5 x$ .

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Step 4.1.2.1

Subtract $5 x$ from $5 x$ .

$0 + 9 = 4$

Step 4.1.2.2

Add $0$ and $9$ .

$9 = 4$

Step 4.2

Since $9 \neq 4$ , there are no solutions.

No solution