Solve for x (x+9)/6=19/15-(x-3)/5

$\frac{x + 9}{6} = \frac{19}{15} - \frac{x - 3}{5}$

Step 1

Multiply both sides by $6$ .

$\frac{x + 9}{6} \cdot 6 = (\frac{19}{15} - \frac{x - 3}{5}) \cdot 6$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{x + 9}{6} \cdot 6 = (\frac{19}{15} - \frac{x - 3}{5}) \cdot 6$

Rewrite the expression.

$x + 9 = (\frac{19}{15} - \frac{x - 3}{5}) \cdot 6$

Simplify the right side.

Simplify $(\frac{19}{15} - \frac{x - 3}{5}) \cdot 6$ .

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

$x + 9 = (\frac{19}{15} - \frac{x - 3}{5} \cdot \frac{3}{3}) \cdot 6$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - 3}{5}$ by $\frac{3}{3}$ .

$x + 9 = (\frac{19}{15} - \frac{(x - 3) \cdot 3}{5 \cdot 3}) \cdot 6$

Multiply $5$ by $3$ .

$x + 9 = (\frac{19}{15} - \frac{(x - 3) \cdot 3}{15}) \cdot 6$

Combine the numerators over the common denominator.

$x + 9 = \frac{19 - (x - 3) \cdot 3}{15} \cdot 6$

Simplify the numerator.

Apply the distributive property.

$x + 9 = \frac{19 + (- x - - 3) \cdot 3}{15} \cdot 6$

Multiply $- 1$ by $- 3$ .

$x + 9 = \frac{19 + (- x + 3) \cdot 3}{15} \cdot 6$

Apply the distributive property.

$x + 9 = \frac{19 - x \cdot 3 + 3 \cdot 3}{15} \cdot 6$

Multiply $3$ by $- 1$ .

$x + 9 = \frac{19 - 3 x + 3 \cdot 3}{15} \cdot 6$

Multiply $3$ by $3$ .

$x + 9 = \frac{19 - 3 x + 9}{15} \cdot 6$

Add $19$ and $9$ .

$x + 9 = \frac{- 3 x + 28}{15} \cdot 6$

Simplify terms.

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$x + 9 = \frac{- 3 x + 28}{3 (5)} \cdot 6$

Factor $3$ out of $6$ .

$x + 9 = \frac{- 3 x + 28}{3 \cdot 5} \cdot (3 \cdot 2)$

Cancel the common factor.

$x + 9 = \frac{- 3 x + 28}{3 \cdot 5} \cdot (3 \cdot 2)$

Rewrite the expression.

$x + 9 = \frac{- 3 x + 28}{5} \cdot 2$

Combine $\frac{- 3 x + 28}{5}$ and $2$ .

$x + 9 = \frac{(- 3 x + 28) \cdot 2}{5}$

Move $2$ to the left of $- 3 x + 28$ .

$x + 9 = \frac{2 \cdot (- 3 x + 28)}{5}$

Factor $- 1$ out of $- 3 x$ .

$x + 9 = \frac{2 (- (3 x) + 28)}{5}$

Rewrite $28$ as $- 1 (- 28)$ .

$x + 9 = \frac{2 (- (3 x) - 1 (- 28))}{5}$

Factor $- 1$ out of $- (3 x) - 1 (- 28)$ .

$x + 9 = \frac{2 (- (3 x - 28))}{5}$

Simplify the expression.

Rewrite $- (3 x - 28)$ as $- 1 (3 x - 28)$ .

$x + 9 = \frac{2 (- 1 (3 x - 28))}{5}$

Move the negative in front of the fraction.

$x + 9 = - \frac{2 (3 x - 28)}{5}$

Step 3

Solve for $x$ .

Multiply both sides by $5$ .

$(x + 9) \cdot 5 = - \frac{2 (3 x - 28)}{5} \cdot 5$

Simplify.

Simplify the left side.

Simplify $(x + 9) \cdot 5$ .

Apply the distributive property.

$x \cdot 5 + 9 \cdot 5 = - \frac{2 (3 x - 28)}{5} \cdot 5$

Simplify the expression.

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

$5 \cdot x + 9 \cdot 5 = - \frac{2 (3 x - 28)}{5} \cdot 5$

Multiply $9$ by $5$ .

$5 x + 45 = - \frac{2 (3 x - 28)}{5} \cdot 5$

Simplify the right side.

Simplify $- \frac{2 (3 x - 28)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2 (3 x - 28)}{5}$ into the numerator.

$5 x + 45 = \frac{- 2 (3 x - 28)}{5} \cdot 5$

Cancel the common factor.

$5 x + 45 = \frac{- 2 (3 x - 28)}{5} \cdot 5$

Rewrite the expression.

$5 x + 45 = - 2 (3 x - 28)$

Apply the distributive property.

$5 x + 45 = - 2 (3 x) - 2 \cdot - 28$

Multiply.

Multiply $3$ by $- 2$ .

$5 x + 45 = - 6 x - 2 \cdot - 28$

Multiply $- 2$ by $- 28$ .

$5 x + 45 = - 6 x + 56$

Solve for $x$ .

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

Add $6 x$ to both sides of the equation.

$5 x + 45 + 6 x = 56$

Add $5 x$ and $6 x$ .

$11 x + 45 = 56$

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

Subtract $45$ from both sides of the equation.

$11 x = 56 - 45$

Subtract $45$ from $56$ .

$11 x = 11$

Divide each term in $11 x = 11$ by $11$ and simplify.

Divide each term in $11 x = 11$ by $11$ .

$\frac{11 x}{11} = \frac{11}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{11}{11}$

Divide $x$ by $1$ .

$x = \frac{11}{11}$

Simplify the right side.

Divide $11$ by $11$ .

$x = 1$

Solve for x (x+9)/6=19/15-(x-3)/5

Related Questions

Support LCMGCF.com by disabling your adblocker.