Solve for x (x+1)/2+(5x-2)/3=0

$\frac{x + 1}{2} + \frac{5 x - 2}{3} = 0$

Simplify $\frac{x + 1}{2} + \frac{5 x - 2}{3}$ .

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

$\frac{x + 1}{2} \cdot \frac{3}{3} + \frac{5 x - 2}{3} = 0$

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

$\frac{x + 1}{2} \cdot \frac{3}{3} + \frac{5 x - 2}{3} \cdot \frac{2}{2} = 0$

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

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

$\frac{(x + 1) \cdot 3}{2 \cdot 3} + \frac{5 x - 2}{3} \cdot \frac{2}{2} = 0$

Multiply $2$ by $3$ .

$\frac{(x + 1) \cdot 3}{6} + \frac{5 x - 2}{3} \cdot \frac{2}{2} = 0$

Multiply $\frac{5 x - 2}{3}$ by $\frac{2}{2}$ .

$\frac{(x + 1) \cdot 3}{6} + \frac{(5 x - 2) \cdot 2}{3 \cdot 2} = 0$

Multiply $3$ by $2$ .

$\frac{(x + 1) \cdot 3}{6} + \frac{(5 x - 2) \cdot 2}{6} = 0$

Combine the numerators over the common denominator.

$\frac{(x + 1) \cdot 3 + (5 x - 2) \cdot 2}{6} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 3 + 1 \cdot 3 + (5 x - 2) \cdot 2}{6} = 0$

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

$\frac{3 \cdot x + 1 \cdot 3 + (5 x - 2) \cdot 2}{6} = 0$

Multiply $3$ by $1$ .

$\frac{3 \cdot x + 3 + (5 x - 2) \cdot 2}{6} = 0$

Apply the distributive property.

$\frac{3 x + 3 + 5 x \cdot 2 - 2 \cdot 2}{6} = 0$

Multiply $2$ by $5$ .

$\frac{3 x + 3 + 10 x - 2 \cdot 2}{6} = 0$

Multiply $- 2$ by $2$ .

$\frac{3 x + 3 + 10 x - 4}{6} = 0$

Add $3 x$ and $10 x$ .

$\frac{13 x + 3 - 4}{6} = 0$

Subtract $4$ from $3$ .

$\frac{13 x - 1}{6} = 0$

Set the numerator equal to zero.

$13 x - 1 = 0$

Solve the equation for $x$ .

Add $1$ to both sides of the equation.

$13 x = 1$

Divide each term in $13 x = 1$ by $13$ and simplify.

Divide each term in $13 x = 1$ by $13$ .

$\frac{13 x}{13} = \frac{1}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{1}{13}$

Divide $x$ by $1$ .

$x = \frac{1}{13}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{13}$

Decimal Form:

$x = 0.\overline{076923}$

Solve for x (x+1)/2+(5x-2)/3=0

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