Solve for x (2x-3)/10+1/2=x+1

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

Simplify $\frac{2 x - 3}{10} + \frac{1}{2}$ .

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

$\frac{2 x - 3}{10} + \frac{1}{2} \cdot \frac{5}{5} = x + 1$

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

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

$\frac{2 x - 3}{10} + \frac{5}{2 \cdot 5} = x + 1$

Multiply $2$ by $5$ .

$\frac{2 x - 3}{10} + \frac{5}{10} = x + 1$

Combine the numerators over the common denominator.

$\frac{2 x - 3 + 5}{10} = x + 1$

Simplify the numerator.

Add $- 3$ and $5$ .

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

Factor $2$ out of $2 x + 2$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $2$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Subtract $x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $- 1$ .

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

Subtract $5 x$ from $x$ .

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

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) + 1}{5} = 1$

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

$\frac{- (4 x) - 1 (- 1)}{5} = 1$

Factor $- 1$ out of $- (4 x) - 1 (- 1)$ .

$\frac{- (4 x - 1)}{5} = 1$

Rewrite $- (4 x - 1)$ as $- 1 (4 x - 1)$ .

$\frac{- 1 (4 x - 1)}{5} = 1$

Move the negative in front of the fraction.

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

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{4 x - 1}{5}) = - 5 \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{4 x - 1}{5}$ into the numerator.

$- 5 \frac{- (4 x - 1)}{5} = - 5 \cdot 1$

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- (4 x - 1)}{5} = - 5 \cdot 1$

Cancel the common factor.

$5 \cdot - 1 \frac{- (4 x - 1)}{5} = - 5 \cdot 1$

Rewrite the expression.

$- - (4 x - 1) = - 5 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (4 x - 1) = - 5 \cdot 1$

Multiply $4 x - 1$ by $1$ .

$4 x - 1 = - 5 \cdot 1$

Simplify the right side.

Multiply $- 5$ by $1$ .

$4 x - 1 = - 5$

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

Add $1$ to both sides of the equation.

$4 x = - 5 + 1$

Add $- 5$ and $1$ .

$4 x = - 4$

Divide each term in $4 x = - 4$ by $4$ and simplify.

Divide each term in $4 x = - 4$ by $4$ .

$\frac{4 x}{4} = \frac{- 4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 4}{4}$

Divide $x$ by $1$ .

$x = \frac{- 4}{4}$

Simplify the right side.

Divide $- 4$ by $4$ .

$x = - 1$

Solve for x (2x-3)/10+1/2=x+1

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