Solve 2x-(7-5x)/9x-(3+4x)=7/6f

$$\frac { 2 x - ( 7 - 5 x ) } { 9 x - ( 3 + 4 x ) } = \frac { 7 } { 6 } f$$

Solve for f

$$f=-\frac{6\left(x-1\right)}{3-5x}$$

$$x\neq \frac{3}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6\left(5x-3\right), the least common multiple of 9x-\left(3+4x\right),6.

$$6\left(2x-\left(7-5x\right)\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

To find the opposite of 7-5x, find the opposite of each term.

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

Combine 2x and 5x to get 7x.

$$6\left(7x-7\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Use the distributive property to multiply 6 by 7x-7.

$$42x-42=\frac{7}{6}f\times 6\left(5x-3\right)$$

Multiply \frac{7}{6} and 6 to get 7.

$$42x-42=7f\left(5x-3\right)$$

Use the distributive property to multiply 7f by 5x-3.

$$42x-42=35xf-21f$$

Swap sides so that all variable terms are on the left hand side.

$$35xf-21f=42x-42$$

Combine all terms containing f.

$$\left(35x-21\right)f=42x-42$$

Divide both sides by 35x-21.

$$\frac{\left(35x-21\right)f}{35x-21}=\frac{42x-42}{35x-21}$$

Dividing by 35x-21 undoes the multiplication by 35x-21.

$$f=\frac{42x-42}{35x-21}$$

Divide -42+42x by 35x-21.

$$f=\frac{6\left(x-1\right)}{5x-3}$$

Solve for x

$$x=-\frac{3\left(f-2\right)}{6-5f}$$

$$f\neq \frac{6}{5}$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{3}{5} since division by zero is not defined. Multiply both sides of the equation by 6\left(5x-3\right), the least common multiple of 9x-\left(3+4x\right),6.

$$6\left(2x-\left(7-5x\right)\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

To find the opposite of 7-5x, find the opposite of each term.

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

Combine 2x and 5x to get 7x.

$$6\left(7x-7\right)=\frac{7}{6}f\times 6\left(5x-3\right)$$

Use the distributive property to multiply 6 by 7x-7.

$$42x-42=\frac{7}{6}f\times 6\left(5x-3\right)$$

Multiply \frac{7}{6} and 6 to get 7.

$$42x-42=7f\left(5x-3\right)$$

Use the distributive property to multiply 7f by 5x-3.

$$42x-42=35fx-21f$$

Subtract 35fx from both sides.

$$42x-42-35fx=-21f$$

Add 42 to both sides.

$$42x-35fx=-21f+42$$

Combine all terms containing x.

$$\left(42-35f\right)x=-21f+42$$

The equation is in standard form.

$$\left(42-35f\right)x=42-21f$$

Divide both sides by 42-35f.

$$\frac{\left(42-35f\right)x}{42-35f}=\frac{42-21f}{42-35f}$$

Dividing by 42-35f undoes the multiplication by 42-35f.

$$x=\frac{42-21f}{42-35f}$$

Divide -21f+42 by 42-35f.

$$x=\frac{3\left(2-f\right)}{6-5f}$$

Variable x cannot be equal to \frac{3}{5}.

$$x=\frac{3\left(2-f\right)}{6-5f}\text{, }x\neq \frac{3}{5}$$