Solve for x -1+(x+3)/8=(3x+7)/40

$- 1 + \frac{x + 3}{8} = \frac{3 x + 7}{40}$

Multiply both sides by $40$ .

$(- 1 + \frac{x + 3}{8}) \cdot 40 = \frac{3 x + 7}{40} \cdot 40$

Simplify.

Simplify the left side.

Simplify $(- 1 + \frac{x + 3}{8}) \cdot 40$ .

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(- 1 \cdot \frac{8}{8} + \frac{x + 3}{8}) \cdot 40 = \frac{3 x + 7}{40} \cdot 40$

Simplify terms.

Combine $- 1$ and $\frac{8}{8}$ .

$(\frac{- 1 \cdot 8}{8} + \frac{x + 3}{8}) \cdot 40 = \frac{3 x + 7}{40} \cdot 40$

Combine the numerators over the common denominator.

$\frac{- 1 \cdot 8 + x + 3}{8} \cdot 40 = \frac{3 x + 7}{40} \cdot 40$

Simplify the numerator.

Multiply $- 1$ by $8$ .

$\frac{- 8 + x + 3}{8} \cdot 40 = \frac{3 x + 7}{40} \cdot 40$

Add $- 8$ and $3$ .

$\frac{x - 5}{8} \cdot 40 = \frac{3 x + 7}{40} \cdot 40$

Simplify terms.

Cancel the common factor of $8$ .

Factor $8$ out of $40$ .

$\frac{x - 5}{8} \cdot (8 (5)) = \frac{3 x + 7}{40} \cdot 40$

Cancel the common factor.

$\frac{x - 5}{8} \cdot (8 \cdot 5) = \frac{3 x + 7}{40} \cdot 40$

Rewrite the expression.

$(x - 5) \cdot 5 = \frac{3 x + 7}{40} \cdot 40$

Apply the distributive property.

$x \cdot 5 - 5 \cdot 5 = \frac{3 x + 7}{40} \cdot 40$

Simplify the expression.

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

$5 \cdot x - 5 \cdot 5 = \frac{3 x + 7}{40} \cdot 40$

Multiply $- 5$ by $5$ .

$5 x - 25 = \frac{3 x + 7}{40} \cdot 40$

Simplify the right side.

Cancel the common factor of $40$ .

Cancel the common factor.

$5 x - 25 = \frac{3 x + 7}{40} \cdot 40$

Rewrite the expression.

$5 x - 25 = 3 x + 7$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$5 x - 25 - 3 x = 7$

Subtract $3 x$ from $5 x$ .

$2 x - 25 = 7$

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

Add $25$ to both sides of the equation.

$2 x = 7 + 25$

Add $7$ and $25$ .

$2 x = 32$

Divide each term in $2 x = 32$ by $2$ and simplify.

Divide each term in $2 x = 32$ by $2$ .

$\frac{2 x}{2} = \frac{32}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{32}{2}$

Divide $x$ by $1$ .

$x = \frac{32}{2}$

Simplify the right side.

Divide $32$ by $2$ .

$x = 16$

Solve for x -1+(x+3)/8=(3x+7)/40

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