Solve for x (3x-8)/6-(5x+3)/3=10/4

$\frac{3 x - 8}{6} - \frac{5 x + 3}{3} = \frac{10}{4}$

Step 1

Simplify $\frac{3 x - 8}{6} - \frac{5 x + 3}{3}$ .

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

$\frac{3 x - 8}{6} - \frac{5 x + 3}{3} \cdot \frac{2}{2} = \frac{10}{4}$

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

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

$\frac{3 x - 8}{6} - \frac{(5 x + 3) \cdot 2}{3 \cdot 2} = \frac{10}{4}$

Multiply $3$ by $2$ .

$\frac{3 x - 8}{6} - \frac{(5 x + 3) \cdot 2}{6} = \frac{10}{4}$

Combine the numerators over the common denominator.

$\frac{3 x - 8 - (5 x + 3) \cdot 2}{6} = \frac{10}{4}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x - 8 + (- (5 x) - 1 \cdot 3) \cdot 2}{6} = \frac{10}{4}$

Multiply $5$ by $- 1$ .

$\frac{3 x - 8 + (- 5 x - 1 \cdot 3) \cdot 2}{6} = \frac{10}{4}$

Multiply $- 1$ by $3$ .

$\frac{3 x - 8 + (- 5 x - 3) \cdot 2}{6} = \frac{10}{4}$

Apply the distributive property.

$\frac{3 x - 8 - 5 x \cdot 2 - 3 \cdot 2}{6} = \frac{10}{4}$

Multiply $2$ by $- 5$ .

$\frac{3 x - 8 - 10 x - 3 \cdot 2}{6} = \frac{10}{4}$

Multiply $- 3$ by $2$ .

$\frac{3 x - 8 - 10 x - 6}{6} = \frac{10}{4}$

Subtract $10 x$ from $3 x$ .

$\frac{- 7 x - 8 - 6}{6} = \frac{10}{4}$

Subtract $6$ from $- 8$ .

$\frac{- 7 x - 14}{6} = \frac{10}{4}$

Factor $7$ out of $- 7 x - 14$ .

Factor $7$ out of $- 7 x$ .

$\frac{7 (- x) - 14}{6} = \frac{10}{4}$

Factor $7$ out of $- 14$ .

$\frac{7 (- x) + 7 (- 2)}{6} = \frac{10}{4}$

Factor $7$ out of $7 (- x) + 7 (- 2)$ .

$\frac{7 (- x - 2)}{6} = \frac{10}{4}$

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

$\frac{7 (- (x) - 2)}{6} = \frac{10}{4}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{7 (- (x) - 1 (2))}{6} = \frac{10}{4}$

Factor $- 1$ out of $- (x) - 1 (2)$ .

$\frac{7 (- (x + 2))}{6} = \frac{10}{4}$

Simplify the expression.

Rewrite $- (x + 2)$ as $- 1 (x + 2)$ .

$\frac{7 (- 1 (x + 2))}{6} = \frac{10}{4}$

Move the negative in front of the fraction.

$- \frac{7 (x + 2)}{6} = \frac{10}{4}$

Step 2

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$- \frac{7 (x + 2)}{6} = \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$- \frac{7 (x + 2)}{6} = \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$- \frac{7 (x + 2)}{6} = \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$- \frac{7 (x + 2)}{6} = \frac{5}{2}$

Step 3

Multiply both sides of the equation by $- \frac{6}{7}$ .

$- \frac{6}{7} (- \frac{7 (x + 2)}{6}) = - \frac{6}{7} \cdot \frac{5}{2}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{7} (- \frac{7 (x + 2)}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$\frac{- 6}{7} (- \frac{7 (x + 2)}{6}) = - \frac{6}{7} \cdot \frac{5}{2}$

Move the leading negative in $- \frac{7 (x + 2)}{6}$ into the numerator.

$\frac{- 6}{7} \cdot \frac{- 7 (x + 2)}{6} = - \frac{6}{7} \cdot \frac{5}{2}$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{7} \cdot \frac{- 7 (x + 2)}{6} = - \frac{6}{7} \cdot \frac{5}{2}$

Cancel the common factor.

$\frac{6 \cdot - 1}{7} \cdot \frac{- 7 (x + 2)}{6} = - \frac{6}{7} \cdot \frac{5}{2}$

Rewrite the expression.

$\frac{- 1}{7} (- 7 (x + 2)) = - \frac{6}{7} \cdot \frac{5}{2}$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 (x + 2)$ .

$\frac{- 1}{7} (7 (- (x + 2))) = - \frac{6}{7} \cdot \frac{5}{2}$

Cancel the common factor.

$\frac{- 1}{7} (7 (- (x + 2))) = - \frac{6}{7} \cdot \frac{5}{2}$

Rewrite the expression.

$- - (x + 2) = - \frac{6}{7} \cdot \frac{5}{2}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (x + 2) = - \frac{6}{7} \cdot \frac{5}{2}$

Multiply $x + 2$ by $1$ .

$x + 2 = - \frac{6}{7} \cdot \frac{5}{2}$

Simplify the right side.

Simplify $- \frac{6}{7} \cdot \frac{5}{2}$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$x + 2 = \frac{- 6}{7} \cdot \frac{5}{2}$

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

$x + 2 = \frac{2 \cdot - 3}{7} \cdot \frac{5}{2}$

Rewrite the expression.

$x + 2 = \frac{- 3}{7} \cdot 5$

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

$x + 2 = \frac{- 3 \cdot 5}{7}$

Simplify the expression.

Multiply $- 3$ by $5$ .

$x + 2 = \frac{- 15}{7}$

Move the negative in front of the fraction.

$x + 2 = - \frac{15}{7}$

Step 5

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

Subtract $2$ from both sides of the equation.

$x = - \frac{15}{7} - 2$

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

$x = - \frac{15}{7} - 2 \cdot \frac{7}{7}$

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

$x = - \frac{15}{7} + \frac{- 2 \cdot 7}{7}$

Combine the numerators over the common denominator.

$x = \frac{- 15 - 2 \cdot 7}{7}$

Simplify the numerator.

Multiply $- 2$ by $7$ .

$x = \frac{- 15 - 14}{7}$

Subtract $14$ from $- 15$ .

$x = \frac{- 29}{7}$

Move the negative in front of the fraction.

$x = - \frac{29}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{29}{7}$

Decimal Form:

$x = - 4.\overline{142857}$

Mixed Number Form:

$x = - 4 \frac{1}{7}$

Solve for x (3x-8)/6-(5x+3)/3=10/4

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