Solve for x (6x-5)/7=(2x-1)/3+2

$\frac{6 x - 5}{7} = \frac{2 x - 1}{3} + 2$

Step 1

Multiply both sides by $7$ .

$\frac{6 x - 5}{7} \cdot 7 = (\frac{2 x - 1}{3} + 2) \cdot 7$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{6 x - 5}{7} \cdot 7 = (\frac{2 x - 1}{3} + 2) \cdot 7$

Rewrite the expression.

$6 x - 5 = (\frac{2 x - 1}{3} + 2) \cdot 7$

Simplify the right side.

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

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

$6 x - 5 = (\frac{2 x - 1}{3} + 2 \cdot \frac{3}{3}) \cdot 7$

Simplify terms.

Combine $2$ and $\frac{3}{3}$ .

$6 x - 5 = (\frac{2 x - 1}{3} + \frac{2 \cdot 3}{3}) \cdot 7$

Combine the numerators over the common denominator.

$6 x - 5 = \frac{2 x - 1 + 2 \cdot 3}{3} \cdot 7$

Simplify the numerator.

Multiply $2$ by $3$ .

$6 x - 5 = \frac{2 x - 1 + 6}{3} \cdot 7$

Add $- 1$ and $6$ .

$6 x - 5 = \frac{2 x + 5}{3} \cdot 7$

Combine fractions.

Combine $\frac{2 x + 5}{3}$ and $7$ .

$6 x - 5 = \frac{(2 x + 5) \cdot 7}{3}$

Move $7$ to the left of $2 x + 5$ .

$6 x - 5 = \frac{7 (2 x + 5)}{3}$

Step 3

Solve for $x$ .

Multiply both sides by $3$ .

$(6 x - 5) \cdot 3 = \frac{7 (2 x + 5)}{3} \cdot 3$

Simplify.

Simplify the left side.

Simplify $(6 x - 5) \cdot 3$ .

Apply the distributive property.

$6 x \cdot 3 - 5 \cdot 3 = \frac{7 (2 x + 5)}{3} \cdot 3$

Multiply.

Multiply $3$ by $6$ .

$18 x - 5 \cdot 3 = \frac{7 (2 x + 5)}{3} \cdot 3$

Multiply $- 5$ by $3$ .

$18 x - 15 = \frac{7 (2 x + 5)}{3} \cdot 3$

Simplify the right side.

Simplify $\frac{7 (2 x + 5)}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$18 x - 15 = \frac{7 (2 x + 5)}{3} \cdot 3$

Rewrite the expression.

$18 x - 15 = 7 (2 x + 5)$

Apply the distributive property.

$18 x - 15 = 7 (2 x) + 7 \cdot 5$

Multiply.

Multiply $2$ by $7$ .

$18 x - 15 = 14 x + 7 \cdot 5$

Multiply $7$ by $5$ .

$18 x - 15 = 14 x + 35$

Solve for $x$ .

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

Subtract $14 x$ from both sides of the equation.

$18 x - 15 - 14 x = 35$

Subtract $14 x$ from $18 x$ .

$4 x - 15 = 35$

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

Add $15$ to both sides of the equation.

$4 x = 35 + 15$

Add $35$ and $15$ .

$4 x = 50$

Divide each term in $4 x = 50$ by $4$ and simplify.

Divide each term in $4 x = 50$ by $4$ .

$\frac{4 x}{4} = \frac{50}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{50}{4}$

Divide $x$ by $1$ .

$x = \frac{50}{4}$

Simplify the right side.

Cancel the common factor of $50$ and $4$ .

Factor $2$ out of $50$ .

$x = \frac{2 (25)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 25}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 25}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{25}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{2}$

Decimal Form:

$x = 12.5$

Mixed Number Form:

$x = 12 \frac{1}{2}$

Solve for x (6x-5)/7=(2x-1)/3+2

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