Solve by Factoring 2/7=(6x)/(4x+17)

$\frac{2}{7} = \frac{6 x}{4 x + 17}$

Step 1

Subtract $\frac{6 x}{4 x + 17}$ from both sides of the equation.

$\frac{2}{7} - \frac{6 x}{4 x + 17} = 0$

Step 2

Simplify $\frac{2}{7} - \frac{6 x}{4 x + 17}$ .

To write $\frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{4 x + 17}{4 x + 17}$ .

$\frac{2}{7} \cdot \frac{4 x + 17}{4 x + 17} - \frac{6 x}{4 x + 17} = 0$

To write $- \frac{6 x}{4 x + 17}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2}{7} \cdot \frac{4 x + 17}{4 x + 17} - \frac{6 x}{4 x + 17} \cdot \frac{7}{7} = 0$

Write each expression with a common denominator of $7 (4 x + 17)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{7}$ by $\frac{4 x + 17}{4 x + 17}$ .

$\frac{2 (4 x + 17)}{7 (4 x + 17)} - \frac{6 x}{4 x + 17} \cdot \frac{7}{7} = 0$

Multiply $\frac{6 x}{4 x + 17}$ by $\frac{7}{7}$ .

$\frac{2 (4 x + 17)}{7 (4 x + 17)} - \frac{6 x \cdot 7}{(4 x + 17) \cdot 7} = 0$

Reorder the factors of $(4 x + 17) \cdot 7$ .

$\frac{2 (4 x + 17)}{7 (4 x + 17)} - \frac{6 x \cdot 7}{7 (4 x + 17)} = 0$

Combine the numerators over the common denominator.

$\frac{2 (4 x + 17) - 6 x \cdot 7}{7 (4 x + 17)} = 0$

Simplify the numerator.

Factor $2$ out of $2 (4 x + 17) - 6 x \cdot 7$ .

Factor $2$ out of $- 6 x \cdot 7$ .

$\frac{2 (4 x + 17) + 2 (- 3 x \cdot 7)}{7 (4 x + 17)} = 0$

Factor $2$ out of $2 (4 x + 17) + 2 (- 3 x \cdot 7)$ .

$\frac{2 (4 x + 17 - 3 x \cdot 7)}{7 (4 x + 17)} = 0$

Multiply $7$ by $- 3$ .

$\frac{2 (4 x + 17 - 21 x)}{7 (4 x + 17)} = 0$

Subtract $21 x$ from $4 x$ .

$\frac{2 (- 17 x + 17)}{7 (4 x + 17)} = 0$

Factor $17$ out of $- 17 x + 17$ .

Factor $17$ out of $- 17 x$ .

$\frac{2 (17 (- x) + 17)}{7 (4 x + 17)} = 0$

Factor $17$ out of $17$ .

$\frac{2 (17 (- x) + 17 (1))}{7 (4 x + 17)} = 0$

Factor $17$ out of $17 (- x) + 17 (1)$ .

$\frac{2 (17 (- x + 1))}{7 (4 x + 17)} = 0$

$\frac{2 \cdot 17 (- x + 1)}{7 (4 x + 17)} = 0$

Multiply $2$ by $17$ .

$\frac{34 (- x + 1)}{7 (4 x + 17)} = 0$

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

$\frac{34 (- (x) + 1)}{7 (4 x + 17)} = 0$

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

$\frac{34 (- (x) - 1 (- 1))}{7 (4 x + 17)} = 0$

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

$\frac{34 (- (x - 1))}{7 (4 x + 17)} = 0$

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

$\frac{34 (- 1 (x - 1))}{7 (4 x + 17)} = 0$

Move the negative in front of the fraction.

$- \frac{34 (x - 1)}{7 (4 x + 17)} = 0$

Step 3

Set the numerator equal to zero.

$34 (x - 1) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $34 (x - 1) = 0$ by $34$ and simplify.

Divide each term in $34 (x - 1) = 0$ by $34$ .

$\frac{34 (x - 1)}{34} = \frac{0}{34}$

Simplify the left side.

Cancel the common factor of $34$ .

Cancel the common factor.

$\frac{34 (x - 1)}{34} = \frac{0}{34}$

Divide $x - 1$ by $1$ .

$x - 1 = \frac{0}{34}$

Simplify the right side.

Divide $0$ by $34$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Solve by Factoring 2/7=(6x)/(4x+17)

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