Solve for x (10x+3)/3-(3x-1)/5=x-2

$\frac{10 x + 3}{3} - \frac{3 x - 1}{5} = x - 2$

Simplify $\frac{10 x + 3}{3} - \frac{3 x - 1}{5}$ .

To write $\frac{10 x + 3}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{10 x + 3}{3} \cdot \frac{5}{5} - \frac{3 x - 1}{5} = x - 2$

To write $- \frac{3 x - 1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10 x + 3}{3} \cdot \frac{5}{5} - \frac{3 x - 1}{5} \cdot \frac{3}{3} = x - 2$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{10 x + 3}{3}$ by $\frac{5}{5}$ .

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

Multiply $3$ by $5$ .

$\frac{(10 x + 3) \cdot 5}{15} - \frac{3 x - 1}{5} \cdot \frac{3}{3} = x - 2$

Multiply $\frac{3 x - 1}{5}$ by $\frac{3}{3}$ .

$\frac{(10 x + 3) \cdot 5}{15} - \frac{(3 x - 1) \cdot 3}{5 \cdot 3} = x - 2$

Multiply $5$ by $3$ .

$\frac{(10 x + 3) \cdot 5}{15} - \frac{(3 x - 1) \cdot 3}{15} = x - 2$

Combine the numerators over the common denominator.

$\frac{(10 x + 3) \cdot 5 - (3 x - 1) \cdot 3}{15} = x - 2$

Simplify the numerator.

Apply the distributive property.

$\frac{10 x \cdot 5 + 3 \cdot 5 - (3 x - 1) \cdot 3}{15} = x - 2$

Multiply $5$ by $10$ .

$\frac{50 x + 3 \cdot 5 - (3 x - 1) \cdot 3}{15} = x - 2$

Multiply $3$ by $5$ .

$\frac{50 x + 15 - (3 x - 1) \cdot 3}{15} = x - 2$

Apply the distributive property.

$\frac{50 x + 15 + (- (3 x) - - 1) \cdot 3}{15} = x - 2$

Multiply $3$ by $- 1$ .

$\frac{50 x + 15 + (- 3 x - - 1) \cdot 3}{15} = x - 2$

Multiply $- 1$ by $- 1$ .

$\frac{50 x + 15 + (- 3 x + 1) \cdot 3}{15} = x - 2$

Apply the distributive property.

$\frac{50 x + 15 - 3 x \cdot 3 + 1 \cdot 3}{15} = x - 2$

Multiply $3$ by $- 3$ .

$\frac{50 x + 15 - 9 x + 1 \cdot 3}{15} = x - 2$

Multiply $3$ by $1$ .

$\frac{50 x + 15 - 9 x + 3}{15} = x - 2$

Subtract $9 x$ from $50 x$ .

$\frac{41 x + 15 + 3}{15} = x - 2$

Add $15$ and $3$ .

$\frac{41 x + 18}{15} = x - 2$

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$\frac{41 x + 18}{15} - x = - 2$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{41 x + 18}{15} - x \cdot \frac{15}{15} = - 2$

Combine $- x$ and $\frac{15}{15}$ .

$\frac{41 x + 18}{15} + \frac{- x \cdot 15}{15} = - 2$

Combine the numerators over the common denominator.

$\frac{41 x + 18 - x \cdot 15}{15} = - 2$

Simplify the numerator.

Multiply $15$ by $- 1$ .

$\frac{41 x + 18 - 15 x}{15} = - 2$

Subtract $15 x$ from $41 x$ .

$\frac{26 x + 18}{15} = - 2$

Factor $2$ out of $26 x + 18$ .

Factor $2$ out of $26 x$ .

$\frac{2 (13 x) + 18}{15} = - 2$

Factor $2$ out of $18$ .

$\frac{2 (13 x) + 2 (9)}{15} = - 2$

Factor $2$ out of $2 (13 x) + 2 (9)$ .

$\frac{2 (13 x + 9)}{15} = - 2$

Multiply both sides by $15$ .

$\frac{2 (13 x + 9)}{15} \cdot 15 = - 2 \cdot 15$

Simplify.

Simplify the left side.

Simplify $\frac{2 (13 x + 9)}{15} \cdot 15$ .

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{2 (13 x + 9)}{15} \cdot 15 = - 2 \cdot 15$

Rewrite the expression.

$2 (13 x + 9) = - 2 \cdot 15$

Apply the distributive property.

$2 (13 x) + 2 \cdot 9 = - 2 \cdot 15$

Multiply.

Multiply $13$ by $2$ .

$26 x + 2 \cdot 9 = - 2 \cdot 15$

Multiply $2$ by $9$ .

$26 x + 18 = - 2 \cdot 15$

Simplify the right side.

Multiply $- 2$ by $15$ .

$26 x + 18 = - 30$

Solve for $x$ .

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

Subtract $18$ from both sides of the equation.

$26 x = - 30 - 18$

Subtract $18$ from $- 30$ .

$26 x = - 48$

Divide each term in $26 x = - 48$ by $26$ and simplify.

Divide each term in $26 x = - 48$ by $26$ .

$\frac{26 x}{26} = \frac{- 48}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} = \frac{- 48}{26}$

Divide $x$ by $1$ .

$x = \frac{- 48}{26}$

Simplify the right side.

Cancel the common factor of $- 48$ and $26$ .

Factor $2$ out of $- 48$ .

$x = \frac{2 (- 24)}{26}$

Cancel the common factors.

Factor $2$ out of $26$ .

$x = \frac{2 \cdot - 24}{2 \cdot 13}$

Cancel the common factor.

$x = \frac{2 \cdot - 24}{2 \cdot 13}$

Rewrite the expression.

$x = \frac{- 24}{13}$

Move the negative in front of the fraction.

$x = - \frac{24}{13}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{24}{13}$

Decimal Form:

$x = - 1.\overline{846153}$

Mixed Number Form:

$x = - 1 \frac{11}{13}$

Solve for x (10x+3)/3-(3x-1)/5=x-2

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