Pre-Algebra Examples

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

Step 1

Multiply both sides by $5$ .

$(\frac{x}{5} + 1) \cdot 5 = \frac{x}{5} \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{x}{5} + 1) \cdot 5$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

Cancel the common factor.

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

Step 2.1.1.2.2

Rewrite the expression.

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

Step 2.1.1.3

Multiply $5$ by $1$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$x + 5 = x$

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.

$x + 5 - x = 0$

Step 3.1.2

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

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Step 3.1.2.1

Subtract $x$ from $x$ .

$0 + 5 = 0$

Step 3.1.2.2

Add $0$ and $5$ .

$5 = 0$

Step 3.2

Since $5 \neq 0$ , there are no solutions.

No solution