Solve for y (2y)/3-1/6=7/2

$\frac{2 y}{3} - \frac{1}{6} = \frac{7}{2}$

Step 1

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

Add $\frac{1}{6}$ to both sides of the equation.

$\frac{2 y}{3} = \frac{7}{2} + \frac{1}{6}$

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 y}{3} = \frac{7}{2} \cdot \frac{3}{3} + \frac{1}{6}$

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

Multiply $\frac{7}{2}$ by $\frac{3}{3}$ .

$\frac{2 y}{3} = \frac{7 \cdot 3}{2 \cdot 3} + \frac{1}{6}$

Multiply $2$ by $3$ .

$\frac{2 y}{3} = \frac{7 \cdot 3}{6} + \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{2 y}{3} = \frac{7 \cdot 3 + 1}{6}$

Simplify the numerator.

Multiply $7$ by $3$ .

$\frac{2 y}{3} = \frac{21 + 1}{6}$

Add $21$ and $1$ .

$\frac{2 y}{3} = \frac{22}{6}$

Cancel the common factor of $22$ and $6$ .

Factor $2$ out of $22$ .

$\frac{2 y}{3} = \frac{2 (11)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 y}{3} = \frac{2 \cdot 11}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 y}{3} = \frac{2 \cdot 11}{2 \cdot 3}$

Rewrite the expression.

$\frac{2 y}{3} = \frac{11}{3}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$2 y = 11$

Step 3

Divide each term in $2 y = 11$ by $2$ and simplify.

Divide each term in $2 y = 11$ by $2$ .

$\frac{2 y}{2} = \frac{11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{11}{2}$

Divide $y$ by $1$ .

$y = \frac{11}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{11}{2}$

Decimal Form:

$y = 5.5$

Mixed Number Form:

$y = 5 \frac{1}{2}$

Solve for y (2y)/3-1/6=7/2

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