Solve for x 1/5-(x-4)/10=1+(x-2)/2

$\frac{1}{5} - \frac{x - 4}{10} = 1 + \frac{x - 2}{2}$

Step 1

Simplify $\frac{1}{5} - \frac{x - 4}{10}$ .

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{5} \cdot \frac{2}{2} - \frac{x - 4}{10} = 1 + \frac{x - 2}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$\frac{2}{5 \cdot 2} - \frac{x - 4}{10} = 1 + \frac{x - 2}{2}$

Multiply $5$ by $2$ .

$\frac{2}{10} - \frac{x - 4}{10} = 1 + \frac{x - 2}{2}$

Combine the numerators over the common denominator.

$\frac{2 - (x - 4)}{10} = 1 + \frac{x - 2}{2}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 - x - - 4}{10} = 1 + \frac{x - 2}{2}$

Multiply $- 1$ by $- 4$ .

$\frac{2 - x + 4}{10} = 1 + \frac{x - 2}{2}$

Add $2$ and $4$ .

$\frac{- x + 6}{10} = 1 + \frac{x - 2}{2}$

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

$\frac{- (x) + 6}{10} = 1 + \frac{x - 2}{2}$

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{- (x) - 1 (- 6)}{10} = 1 + \frac{x - 2}{2}$

Factor $- 1$ out of $- (x) - 1 (- 6)$ .

$\frac{- (x - 6)}{10} = 1 + \frac{x - 2}{2}$

Simplify the expression.

Rewrite $- (x - 6)$ as $- 1 (x - 6)$ .

$\frac{- 1 (x - 6)}{10} = 1 + \frac{x - 2}{2}$

Move the negative in front of the fraction.

$- \frac{x - 6}{10} = 1 + \frac{x - 2}{2}$

Step 2

Simplify $1 + \frac{x - 2}{2}$ .

Combine into one fraction.

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

$- \frac{x - 6}{10} = \frac{2}{2} + \frac{x - 2}{2}$

Combine the numerators over the common denominator.

$- \frac{x - 6}{10} = \frac{2 + x - 2}{2}$

Simplify the numerator.

Subtract $2$ from $2$ .

$- \frac{x - 6}{10} = \frac{x + 0}{2}$

Add $x$ and $0$ .

$- \frac{x - 6}{10} = \frac{x}{2}$

Step 3

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

Subtract $\frac{x}{2}$ from both sides of the equation.

$- \frac{x - 6}{10} - \frac{x}{2} = 0$

To write $- \frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{x - 6}{10} - \frac{x}{2} \cdot \frac{5}{5} = 0$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{5}{5}$ .

$- \frac{x - 6}{10} - \frac{x \cdot 5}{2 \cdot 5} = 0$

Multiply $2$ by $5$ .

$- \frac{x - 6}{10} - \frac{x \cdot 5}{10} = 0$

Combine the numerators over the common denominator.

$\frac{- (x - 6) - x \cdot 5}{10} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{- x - - 6 - x \cdot 5}{10} = 0$

Multiply $- 1$ by $- 6$ .

$\frac{- x + 6 - x \cdot 5}{10} = 0$

Multiply $5$ by $- 1$ .

$\frac{- x + 6 - 5 x}{10} = 0$

Subtract $5 x$ from $- x$ .

$\frac{- 6 x + 6}{10} = 0$

Factor $6$ out of $- 6 x + 6$ .

Factor $6$ out of $- 6 x$ .

$\frac{6 (- x) + 6}{10} = 0$

Factor $6$ out of $6$ .

$\frac{6 (- x) + 6 (1)}{10} = 0$

Factor $6$ out of $6 (- x) + 6 (1)$ .

$\frac{6 (- x + 1)}{10} = 0$

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

Factor $2$ out of $6 (- x + 1)$ .

$\frac{2 (3 (- x + 1))}{10} = 0$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 (3 (- x + 1))}{2 (5)} = 0$

Cancel the common factor.

$\frac{2 (3 (- x + 1))}{2 \cdot 5} = 0$

Rewrite the expression.

$\frac{3 (- x + 1)}{5} = 0$

Factor $- 1$ out of $- x$ .

$\frac{3 (- (x) + 1)}{5} = 0$

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{3 (- (x) - 1 (- 1))}{5} = 0$

Factor $- 1$ out of $- (x) - 1 (- 1)$ .

$\frac{3 (- (x - 1))}{5} = 0$

Rewrite $- (x - 1)$ as $- 1 (x - 1)$ .

$\frac{3 (- 1 (x - 1))}{5} = 0$

Move the negative in front of the fraction.

$- \frac{3 (x - 1)}{5} = 0$

Step 4

Set the numerator equal to zero.

$3 (x - 1) = 0$

Step 5

Solve the equation for $x$ .

Divide each term in $3 (x - 1) = 0$ by $3$ and simplify.

Divide each term in $3 (x - 1) = 0$ by $3$ .

$\frac{3 (x - 1)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x - 1)}{3} = \frac{0}{3}$

Divide $x - 1$ by $1$ .

$x - 1 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Solve for x 1/5-(x-4)/10=1+(x-2)/2

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