Solve for x 2 1/7+3/7(3x-5)=-4

$2 \frac{1}{7} + \frac{3}{7} (3 x - 5) = - 4$

Simplify the left side.

Simplify $2 \frac{1}{7} + \frac{3}{7} \cdot (3 x - 5)$ .

Convert $2 \frac{1}{7}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$2 + \frac{1}{7} + \frac{3}{7} \cdot (3 x - 5) = - 4$

Add $2$ and $\frac{1}{7}$ .

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

$2 \cdot \frac{7}{7} + \frac{1}{7} + \frac{3}{7} \cdot (3 x - 5) = - 4$

Combine $2$ and $\frac{7}{7}$ .

$\frac{2 \cdot 7}{7} + \frac{1}{7} + \frac{3}{7} \cdot (3 x - 5) = - 4$

Combine the numerators over the common denominator.

$\frac{2 \cdot 7 + 1}{7} + \frac{3}{7} \cdot (3 x - 5) = - 4$

Simplify the numerator.

Multiply $2$ by $7$ .

$\frac{14 + 1}{7} + \frac{3}{7} \cdot (3 x - 5) = - 4$

Add $14$ and $1$ .

$\frac{15}{7} + \frac{3}{7} \cdot (3 x - 5) = - 4$

Simplify each term.

Apply the distributive property.

$\frac{15}{7} + \frac{3}{7} (3 x) + \frac{3}{7} \cdot - 5 = - 4$

Multiply $\frac{3}{7} (3 x)$ .

Combine $3$ and $\frac{3}{7}$ .

$\frac{15}{7} + \frac{3 \cdot 3}{7} x + \frac{3}{7} \cdot - 5 = - 4$

Multiply $3$ by $3$ .

$\frac{15}{7} + \frac{9}{7} x + \frac{3}{7} \cdot - 5 = - 4$

Combine $\frac{9}{7}$ and $x$ .

$\frac{15}{7} + \frac{9 x}{7} + \frac{3}{7} \cdot - 5 = - 4$

Multiply $\frac{3}{7} \cdot - 5$ .

Combine $\frac{3}{7}$ and $- 5$ .

$\frac{15}{7} + \frac{9 x}{7} + \frac{3 \cdot - 5}{7} = - 4$

Multiply $3$ by $- 5$ .

$\frac{15}{7} + \frac{9 x}{7} + \frac{- 15}{7} = - 4$

Move the negative in front of the fraction.

$\frac{15}{7} + \frac{9 x}{7} - \frac{15}{7} = - 4$

Combine the opposite terms in $\frac{15}{7} + \frac{9 x}{7} - \frac{15}{7}$ .

Combine the numerators over the common denominator.

$\frac{9 x}{7} + \frac{15 - 15}{7} = - 4$

Subtract $15$ from $15$ .

$\frac{9 x}{7} + \frac{0}{7} = - 4$

Divide $0$ by $7$ .

$\frac{9 x}{7} + 0 = - 4$

Add $\frac{9 x}{7}$ and $0$ .

$\frac{9 x}{7} = - 4$

Multiply both sides of the equation by $\frac{7}{9}$ .

$\frac{7}{9} \cdot \frac{9 x}{7} = \frac{7}{9} \cdot - 4$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{7}{9} \cdot \frac{9 x}{7}$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7}{9} \cdot \frac{9 x}{7} = \frac{7}{9} \cdot - 4$

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{7}{9} \cdot - 4$

Cancel the common factor of $9$ .

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{7}{9} \cdot - 4$

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{7}{9} \cdot - 4$

Rewrite the expression.

$x = \frac{7}{9} \cdot - 4$

Simplify the right side.

Simplify $\frac{7}{9} \cdot - 4$ .

Multiply $\frac{7}{9} \cdot - 4$ .

Combine $\frac{7}{9}$ and $- 4$ .

$x = \frac{7 \cdot - 4}{9}$

Multiply $7$ by $- 4$ .

$x = \frac{- 28}{9}$

Move the negative in front of the fraction.

$x = - \frac{28}{9}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{28}{9}$

Decimal Form:

$x = - 3.\overline{1}$

Mixed Number Form:

$x = - 3 \frac{1}{9}$

Solve for x 2 1/7+3/7(3x-5)=-4

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