Solve for x -1+5/2=(x+7)/10

$- 1 + \frac{5}{2} = \frac{x + 7}{10}$

Step 1

Rewrite the equation as $\frac{x + 7}{10} = - 1 + \frac{5}{2}$ .

$\frac{x + 7}{10} = - 1 + \frac{5}{2}$

Step 2

Multiply both sides of the equation by $10$ .

$10 \frac{x + 7}{10} = 10 (- 1 + \frac{5}{2})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$10 \frac{x + 7}{10} = 10 (- 1 + \frac{5}{2})$

Rewrite the expression.

$x + 7 = 10 (- 1 + \frac{5}{2})$

Simplify the right side.

Simplify $10 (- 1 + \frac{5}{2})$ .

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

$x + 7 = 10 (- 1 \cdot \frac{2}{2} + \frac{5}{2})$

Combine $- 1$ and $\frac{2}{2}$ .

$x + 7 = 10 (\frac{- 1 \cdot 2}{2} + \frac{5}{2})$

Combine the numerators over the common denominator.

$x + 7 = 10 \frac{- 1 \cdot 2 + 5}{2}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$x + 7 = 10 \frac{- 2 + 5}{2}$

Add $- 2$ and $5$ .

$x + 7 = 10 (\frac{3}{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$x + 7 = 2 (5) \frac{3}{2}$

Cancel the common factor.

$x + 7 = 2 \cdot 5 \frac{3}{2}$

Rewrite the expression.

$x + 7 = 5 \cdot 3$

Multiply $5$ by $3$ .

$x + 7 = 15$

Step 4

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

Subtract $7$ from both sides of the equation.

$x = 15 - 7$

Subtract $7$ from $15$ .

$x = 8$