Solve for x 3x-(2x)/5=(3x)/10+14

$3 x - \frac{2 x}{5} = \frac{3 x}{10} + 14$

Step 1

Simplify $3 x - \frac{2 x}{5}$ .

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

$3 x \cdot \frac{5}{5} - \frac{2 x}{5} = \frac{3 x}{10} + 14$

Simplify terms.

Combine $3 x$ and $\frac{5}{5}$ .

$\frac{3 x \cdot 5}{5} - \frac{2 x}{5} = \frac{3 x}{10} + 14$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 5 - 2 x}{5} = \frac{3 x}{10} + 14$

Simplify the numerator.

Factor $x$ out of $3 x \cdot 5 - 2 x$ .

Factor $x$ out of $3 x \cdot 5$ .

$\frac{x (3 \cdot 5) - 2 x}{5} = \frac{3 x}{10} + 14$

Factor $x$ out of $- 2 x$ .

$\frac{x (3 \cdot 5) + x \cdot - 2}{5} = \frac{3 x}{10} + 14$

Factor $x$ out of $x (3 \cdot 5) + x \cdot - 2$ .

$\frac{x (3 \cdot 5 - 2)}{5} = \frac{3 x}{10} + 14$

Multiply $3$ by $5$ .

$\frac{x (15 - 2)}{5} = \frac{3 x}{10} + 14$

Subtract $2$ from $15$ .

$\frac{x \cdot 13}{5} = \frac{3 x}{10} + 14$

Move $13$ to the left of $x$ .

$\frac{13 x}{5} = \frac{3 x}{10} + 14$

Step 2

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

Subtract $\frac{3 x}{10}$ from both sides of the equation.

$\frac{13 x}{5} - \frac{3 x}{10} = 14$

To write $\frac{13 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13 x}{5} \cdot \frac{2}{2} - \frac{3 x}{10} = 14$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{13 x}{5}$ by $\frac{2}{2}$ .

$\frac{13 x \cdot 2}{5 \cdot 2} - \frac{3 x}{10} = 14$

Multiply $5$ by $2$ .

$\frac{13 x \cdot 2}{10} - \frac{3 x}{10} = 14$

Combine the numerators over the common denominator.

$\frac{13 x \cdot 2 - 3 x}{10} = 14$

Simplify the numerator.

Factor $x$ out of $13 x \cdot 2 - 3 x$ .

Factor $x$ out of $13 x \cdot 2$ .

$\frac{x (13 \cdot 2) - 3 x}{10} = 14$

Factor $x$ out of $- 3 x$ .

$\frac{x (13 \cdot 2) + x \cdot - 3}{10} = 14$

Factor $x$ out of $x (13 \cdot 2) + x \cdot - 3$ .

$\frac{x (13 \cdot 2 - 3)}{10} = 14$

Multiply $13$ by $2$ .

$\frac{x (26 - 3)}{10} = 14$

Subtract $3$ from $26$ .

$\frac{x \cdot 23}{10} = 14$

Move $23$ to the left of $x$ .

$\frac{23 x}{10} = 14$

Step 3

Multiply both sides of the equation by $\frac{10}{23}$ .

$\frac{10}{23} \cdot \frac{23 x}{10} = \frac{10}{23} \cdot 14$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{10}{23} \cdot \frac{23 x}{10}$ .

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10}{23} \cdot \frac{23 x}{10} = \frac{10}{23} \cdot 14$

Rewrite the expression.

$\frac{1}{23} (23 x) = \frac{10}{23} \cdot 14$

Cancel the common factor of $23$ .

Factor $23$ out of $23 x$ .

$\frac{1}{23} (23 (x)) = \frac{10}{23} \cdot 14$

Cancel the common factor.

$\frac{1}{23} (23 x) = \frac{10}{23} \cdot 14$

Rewrite the expression.

$x = \frac{10}{23} \cdot 14$

Simplify the right side.

Multiply $\frac{10}{23} \cdot 14$ .

Combine $\frac{10}{23}$ and $14$ .

$x = \frac{10 \cdot 14}{23}$

Multiply $10$ by $14$ .

$x = \frac{140}{23}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{140}{23}$

Decimal Form:

$x = 6.08695652 \dots$

Mixed Number Form:

$x = 6 \frac{2}{23}$

Solve for x 3x-(2x)/5=(3x)/10+14

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