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

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

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

Apply the distributive property.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $\frac{3}{2} \cdot 5$ .

Combine $\frac{3}{2}$ and $5$ .

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

Multiply $3$ by $5$ .

$3 x + 1 = \frac{15}{2}$

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

Subtract $1$ from both sides of the equation.

$3 x = \frac{15}{2} - 1$

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

$3 x = \frac{15}{2} - 1 \cdot \frac{2}{2}$

Combine $- 1$ and $\frac{2}{2}$ .

$3 x = \frac{15}{2} + \frac{- 1 \cdot 2}{2}$

Combine the numerators over the common denominator.

$3 x = \frac{15 - 1 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$3 x = \frac{15 - 2}{2}$

Subtract $2$ from $15$ .

$3 x = \frac{13}{2}$

Divide each term in $3 x = \frac{13}{2}$ by $3$ and simplify.

Divide each term in $3 x = \frac{13}{2}$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{13}{2}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{13}{2}}{3}$

Divide $x$ by $1$ .

$x = \frac{\frac{13}{2}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{13}{2} \cdot \frac{1}{3}$

Multiply $\frac{13}{2} \cdot \frac{1}{3}$ .

Multiply $\frac{13}{2}$ by $\frac{1}{3}$ .

$x = \frac{13}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{13}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{6}$

Decimal Form:

$x = 2.1\overline{6}$

Mixed Number Form:

$x = 2 \frac{1}{6}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.