Solve for x (2x+1)/2+x/3=5/6

$\frac{2 x + 1}{2} + \frac{x}{3} = \frac{5}{6}$

Simplify $\frac{2 x + 1}{2} + \frac{x}{3}$ .

To write $\frac{2 x + 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x + 1}{2} \cdot \frac{3}{3} + \frac{x}{3} = \frac{5}{6}$

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

$\frac{2 x + 1}{2} \cdot \frac{3}{3} + \frac{x}{3} \cdot \frac{2}{2} = \frac{5}{6}$

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

Multiply $\frac{2 x + 1}{2}$ by $\frac{3}{3}$ .

$\frac{(2 x + 1) \cdot 3}{2 \cdot 3} + \frac{x}{3} \cdot \frac{2}{2} = \frac{5}{6}$

Multiply $2$ by $3$ .

$\frac{(2 x + 1) \cdot 3}{6} + \frac{x}{3} \cdot \frac{2}{2} = \frac{5}{6}$

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

$\frac{(2 x + 1) \cdot 3}{6} + \frac{x \cdot 2}{3 \cdot 2} = \frac{5}{6}$

Multiply $3$ by $2$ .

$\frac{(2 x + 1) \cdot 3}{6} + \frac{x \cdot 2}{6} = \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{(2 x + 1) \cdot 3 + x \cdot 2}{6} = \frac{5}{6}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 x \cdot 3 + 1 \cdot 3 + x \cdot 2}{6} = \frac{5}{6}$

Multiply $3$ by $2$ .

$\frac{6 x + 1 \cdot 3 + x \cdot 2}{6} = \frac{5}{6}$

Multiply $3$ by $1$ .

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

Move $2$ to the left of $x$ .

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

Add $6 x$ and $2 x$ .

$\frac{8 x + 3}{6} = \frac{5}{6}$

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

$8 x + 3 = 5$

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

Subtract $3$ from both sides of the equation.

$8 x = 5 - 3$

Subtract $3$ from $5$ .

$8 x = 2$

Divide each term in $8 x = 2$ by $8$ and simplify.

Divide each term in $8 x = 2$ by $8$ .

$\frac{8 x}{8} = \frac{2}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{2}{8}$

Divide $x$ by $1$ .

$x = \frac{2}{8}$

Simplify the right side.

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 1}{2 \cdot 4}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 4}$

Rewrite the expression.

$x = \frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}$

Decimal Form:

$x = 0.25$

Solve for x (2x+1)/2+x/3=5/6

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