Solve varphi4x/9-2*(3x-2)/15=x+1/6

$$\varphi \frac { 4 x } { 9 } - \frac { 2 \cdot ( 3 x - 2 ) } { 15 } = \frac { x + 1 } { 6 }$$

Solve for x

$$x=-\frac{9}{40\phi -51}$$

$$\phi \neq \frac{51}{40}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 90, the least common multiple of 9,15,6.

$$10\phi \times 4x-6\times 2\left(3x-2\right)=15\left(x+1\right)$$

Multiply 10 and 4 to get 40.

$$40\phi x-6\times 2\left(3x-2\right)=15\left(x+1\right)$$

Multiply -6 and 2 to get -12.

$$40\phi x-12\left(3x-2\right)=15\left(x+1\right)$$

Use the distributive property to multiply -12 by 3x-2.

$$40\phi x-36x+24=15\left(x+1\right)$$

Use the distributive property to multiply 15 by x+1.

$$40\phi x-36x+24=15x+15$$

Subtract 15x from both sides.

$$40\phi x-36x+24-15x=15$$

Combine -36x and -15x to get -51x.

$$40\phi x-51x+24=15$$

Subtract 24 from both sides.

$$40\phi x-51x=15-24$$

Subtract 24 from 15 to get -9.

$$40\phi x-51x=-9$$

Combine all terms containing x.

$$\left(40\phi -51\right)x=-9$$

Divide both sides by 40\phi -51.

$$\frac{\left(40\phi -51\right)x}{40\phi -51}=-\frac{9}{40\phi -51}$$

Dividing by 40\phi -51 undoes the multiplication by 40\phi -51.

$$x=-\frac{9}{40\phi -51}$$

Solve for φ

$$\phi =\frac{51}{40}-\frac{9}{40x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 90, the least common multiple of 9,15,6.

$$10\phi \times 4x-6\times 2\left(3x-2\right)=15\left(x+1\right)$$

Multiply 10 and 4 to get 40.

$$40\phi x-6\times 2\left(3x-2\right)=15\left(x+1\right)$$

Multiply -6 and 2 to get -12.

$$40\phi x-12\left(3x-2\right)=15\left(x+1\right)$$

Use the distributive property to multiply -12 by 3x-2.

$$40\phi x-36x+24=15\left(x+1\right)$$

Use the distributive property to multiply 15 by x+1.

$$40\phi x-36x+24=15x+15$$

Add 36x to both sides.

$$40\phi x+24=15x+15+36x$$

Combine 15x and 36x to get 51x.

$$40\phi x+24=51x+15$$

Subtract 24 from both sides.

$$40\phi x=51x+15-24$$

Subtract 24 from 15 to get -9.

$$40\phi x=51x-9$$

The equation is in standard form.

$$40x\phi =51x-9$$

Divide both sides by 40x.

$$\frac{40x\phi }{40x}=\frac{51x-9}{40x}$$

Dividing by 40x undoes the multiplication by 40x.

$$\phi =\frac{51x-9}{40x}$$

Divide 51x-9 by 40x.

$$\phi =\frac{51}{40}-\frac{9}{40x}$$