Solve for x x+1/5(x-1)=1

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

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

Simplify each term.

Apply the distributive property.

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

Combine $\frac{1}{5}$ and $x$ .

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

Combine $\frac{1}{5}$ and $- 1$ .

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

Move the negative in front of the fraction.

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

To write $x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Simplify terms.

Combine $x$ and $\frac{5}{5}$ .

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

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

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

Add $5 x$ and $x$ .

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

Multiply both sides by $5$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$6 x - 1 = 1 \cdot 5$

Simplify the right side.

Multiply $5$ by $1$ .

$6 x - 1 = 5$

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$6 x = 5 + 1$

Add $5$ and $1$ .

$6 x = 6$

Divide each term in $6 x = 6$ by $6$ and simplify.

Divide each term in $6 x = 6$ by $6$ .

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $6$ .

$x = 1$

Solve for x x+1/5(x-1)=1

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