Solve for x 5+(x-2)/3=(x+3)/8

$5 + \frac{x - 2}{3} = \frac{x + 3}{8}$

Step 1

Multiply both sides by $8$ .

$(5 + \frac{x - 2}{3}) \cdot 8 = \frac{x + 3}{8} \cdot 8$

Step 2

Simplify.

Simplify the left side.

Simplify $(5 + \frac{x - 2}{3}) \cdot 8$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(5 \cdot \frac{3}{3} + \frac{x - 2}{3}) \cdot 8 = \frac{x + 3}{8} \cdot 8$

Simplify terms.

Combine $5$ and $\frac{3}{3}$ .

$(\frac{5 \cdot 3}{3} + \frac{x - 2}{3}) \cdot 8 = \frac{x + 3}{8} \cdot 8$

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + x - 2}{3} \cdot 8 = \frac{x + 3}{8} \cdot 8$

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 + x - 2}{3} \cdot 8 = \frac{x + 3}{8} \cdot 8$

Subtract $2$ from $15$ .

$\frac{x + 13}{3} \cdot 8 = \frac{x + 3}{8} \cdot 8$

Combine fractions.

Combine $\frac{x + 13}{3}$ and $8$ .

$\frac{(x + 13) \cdot 8}{3} = \frac{x + 3}{8} \cdot 8$

Move $8$ to the left of $x + 13$ .

$\frac{8 (x + 13)}{3} = \frac{x + 3}{8} \cdot 8$

Simplify the right side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 (x + 13)}{3} = \frac{x + 3}{8} \cdot 8$

Rewrite the expression.

$\frac{8 (x + 13)}{3} = x + 3$

Step 3

Solve for $x$ .

Multiply both sides by $3$ .

$\frac{8 (x + 13)}{3} \cdot 3 = (x + 3) \cdot 3$

Simplify.

Simplify the left side.

Simplify $\frac{8 (x + 13)}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{8 (x + 13)}{3} \cdot 3 = (x + 3) \cdot 3$

Rewrite the expression.

$8 (x + 13) = (x + 3) \cdot 3$

Apply the distributive property.

$8 x + 8 \cdot 13 = (x + 3) \cdot 3$

Multiply $8$ by $13$ .

$8 x + 104 = (x + 3) \cdot 3$

Simplify the right side.

Simplify $(x + 3) \cdot 3$ .

Apply the distributive property.

$8 x + 104 = x \cdot 3 + 3 \cdot 3$

Simplify the expression.

Move $3$ to the left of $x$ .

$8 x + 104 = 3 \cdot x + 3 \cdot 3$

Multiply $3$ by $3$ .

$8 x + 104 = 3 x + 9$

Solve for $x$ .

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

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

$8 x + 104 - 3 x = 9$

Subtract $3 x$ from $8 x$ .

$5 x + 104 = 9$

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

Subtract $104$ from both sides of the equation.

$5 x = 9 - 104$

Subtract $104$ from $9$ .

$5 x = - 95$

Divide each term in $5 x = - 95$ by $5$ and simplify.

Divide each term in $5 x = - 95$ by $5$ .

$\frac{5 x}{5} = \frac{- 95}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 95}{5}$

Divide $x$ by $1$ .

$x = \frac{- 95}{5}$

Simplify the right side.

Divide $- 95$ by $5$ .

$x = - 19$

Solve for x 5+(x-2)/3=(x+3)/8

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