Solve for x -4/3-(3x+1)/6=7

$\frac{- 4}{3} - \frac{3 x + 1}{6} = 7$

Step 1

Simplify $\frac{- 4}{3} - \frac{3 x + 1}{6}$ .

Move the negative in front of the fraction.

$- \frac{4}{3} - \frac{3 x + 1}{6} = 7$

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{4}{3} \cdot \frac{2}{2} - \frac{3 x + 1}{6} = 7$

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

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$- \frac{4 \cdot 2}{3 \cdot 2} - \frac{3 x + 1}{6} = 7$

Multiply $3$ by $2$ .

$- \frac{4 \cdot 2}{6} - \frac{3 x + 1}{6} = 7$

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 2 - (3 x + 1)}{6} = 7$

Simplify the numerator.

Factor $- 1$ out of $- 4 \cdot 2 - (3 x + 1)$ .

Reorder $- 4 \cdot 2$ and $- (3 x + 1)$ .

$\frac{- (3 x + 1) - 4 \cdot 2}{6} = 7$

Factor $- 1$ out of $- 4 \cdot 2$ .

$\frac{- (3 x + 1) - (4 \cdot 2)}{6} = 7$

Factor $- 1$ out of $- (3 x + 1) - (4 \cdot 2)$ .

$\frac{- (3 x + 1 + 4 \cdot 2)}{6} = 7$

Multiply $4$ by $2$ .

$\frac{- (3 x + 1 + 8)}{6} = 7$

Add $1$ and $8$ .

$\frac{- (3 x + 9)}{6} = 7$

Factor $3$ out of $3 x + 9$ .

Factor $3$ out of $3 x$ .

$\frac{- (3 (x) + 9)}{6} = 7$

Factor $3$ out of $9$ .

$\frac{- (3 x + 3 \cdot 3)}{6} = 7$

Factor $3$ out of $3 x + 3 \cdot 3$ .

$\frac{- (3 (x + 3))}{6} = 7$

$\frac{- 1 \cdot 3 (x + 3)}{6} = 7$

Multiply $- 1$ by $3$ .

$\frac{- 3 (x + 3)}{6} = 7$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3 (x + 3)$ .

$\frac{3 (- (x + 3))}{6} = 7$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- 2$ .

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x + 3}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - (x + 3) = - 2 \cdot 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (x + 3) = - 2 \cdot 7$

Multiply $x + 3$ by $1$ .

$x + 3 = - 2 \cdot 7$

Simplify the right side.

Multiply $- 2$ by $7$ .

$x + 3 = - 14$

Step 4

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

Subtract $3$ from both sides of the equation.

$x = - 14 - 3$

Subtract $3$ from $- 14$ .

$x = - 17$

Solve for x -4/3-(3x+1)/6=7

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