Solve for w (2w+7)/6+(5w+2)/2=5

$\frac{2 w + 7}{6} + \frac{5 w + 2}{2} = 5$

Simplify $\frac{2 w + 7}{6} + \frac{5 w + 2}{2}$ .

To write $\frac{5 w + 2}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 w + 7}{6} + \frac{5 w + 2}{2} \cdot \frac{3}{3} = 5$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 w + 2}{2}$ by $\frac{3}{3}$ .

$\frac{2 w + 7}{6} + \frac{(5 w + 2) \cdot 3}{2 \cdot 3} = 5$

Multiply $2$ by $3$ .

$\frac{2 w + 7}{6} + \frac{(5 w + 2) \cdot 3}{6} = 5$

Combine the numerators over the common denominator.

$\frac{2 w + 7 + (5 w + 2) \cdot 3}{6} = 5$

Simplify the numerator.

Apply the distributive property.

$\frac{2 w + 7 + 5 w \cdot 3 + 2 \cdot 3}{6} = 5$

Multiply $3$ by $5$ .

$\frac{2 w + 7 + 15 w + 2 \cdot 3}{6} = 5$

Multiply $2$ by $3$ .

$\frac{2 w + 7 + 15 w + 6}{6} = 5$

Add $2 w$ and $15 w$ .

$\frac{17 w + 7 + 6}{6} = 5$

Add $7$ and $6$ .

$\frac{17 w + 13}{6} = 5$

Multiply both sides by $6$ .

$\frac{17 w + 13}{6} \cdot 6 = 5 \cdot 6$

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{17 w + 13}{6} \cdot 6 = 5 \cdot 6$

Rewrite the expression.

$17 w + 13 = 5 \cdot 6$

Simplify the right side.

Multiply $5$ by $6$ .

$17 w + 13 = 30$

Solve for $w$ .

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

Subtract $13$ from both sides of the equation.

$17 w = 30 - 13$

Subtract $13$ from $30$ .

$17 w = 17$

Divide each term in $17 w = 17$ by $17$ and simplify.

Divide each term in $17 w = 17$ by $17$ .

$\frac{17 w}{17} = \frac{17}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 w}{17} = \frac{17}{17}$

Divide $w$ by $1$ .

$w = \frac{17}{17}$

Simplify the right side.

Divide $17$ by $17$ .

$w = 1$

Solve for w (2w+7)/6+(5w+2)/2=5

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