Solve for x -1=2x+7/3

$- 1 = 2 x + \frac{7}{3}$

Step 1

Rewrite the equation as $2 x + \frac{7}{3} = - 1$ .

$2 x + \frac{7}{3} = - 1$

Step 2

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

Subtract $\frac{7}{3}$ from both sides of the equation.

$2 x = - 1 - \frac{7}{3}$

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

$2 x = - 1 \cdot \frac{3}{3} - \frac{7}{3}$

Combine $- 1$ and $\frac{3}{3}$ .

$2 x = \frac{- 1 \cdot 3}{3} - \frac{7}{3}$

Combine the numerators over the common denominator.

$2 x = \frac{- 1 \cdot 3 - 7}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$2 x = \frac{- 3 - 7}{3}$

Subtract $7$ from $- 3$ .

$2 x = \frac{- 10}{3}$

Move the negative in front of the fraction.

$2 x = - \frac{10}{3}$

Step 3

Divide each term in $2 x = - \frac{10}{3}$ by $2$ and simplify.

Divide each term in $2 x = - \frac{10}{3}$ by $2$ .

$\frac{2 x}{2} = \frac{- \frac{10}{3}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \frac{10}{3}}{2}$

Divide $x$ by $1$ .

$x = \frac{- \frac{10}{3}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{10}{3} \cdot \frac{1}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$x = \frac{- 10}{3} \cdot \frac{1}{2}$

Factor $2$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{- 5}{3}$

Move the negative in front of the fraction.

$x = - \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{3}$

Decimal Form:

$x = - 1.\overline{6}$

Mixed Number Form:

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

Solve for x -1=2x+7/3

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