Solve k:-5(2x-3)-3(3x-7)=5

$$k : - 5 ( 2 x - 3 ) - 3 ( 3 x - 7 ) = 5$$

Solve for k

$$k=-\frac{5\left(16-9x\right)}{3-2x}$$

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -5.

$$k\left(2x-3\right)+15\left(3x-7\right)=-25$$

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

$$2kx-3k+15\left(3x-7\right)=-25$$

Use the distributive property to multiply 15 by 3x-7.

$$2kx-3k+45x-105=-25$$

Subtract 45x from both sides.

$$2kx-3k-105=-25-45x$$

Add 105 to both sides.

$$2kx-3k=-25-45x+105$$

Add -25 and 105 to get 80.

$$2kx-3k=80-45x$$

Combine all terms containing k.

$$\left(2x-3\right)k=80-45x$$

Divide both sides by 2x-3.

$$\frac{\left(2x-3\right)k}{2x-3}=\frac{80-45x}{2x-3}$$

Dividing by 2x-3 undoes the multiplication by 2x-3.

$$k=\frac{80-45x}{2x-3}$$

Divide -45x+80 by 2x-3.

$$k=\frac{5\left(16-9x\right)}{2x-3}$$

Solve for x

$$x=\frac{3k+80}{2k+45}$$

$$k\neq -\frac{45}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -5.

$$k\left(2x-3\right)+15\left(3x-7\right)=-25$$

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

$$2kx-3k+15\left(3x-7\right)=-25$$

Use the distributive property to multiply 15 by 3x-7.

$$2kx-3k+45x-105=-25$$

Add 3k to both sides.

$$2kx+45x-105=-25+3k$$

Add 105 to both sides.

$$2kx+45x=-25+3k+105$$

Add -25 and 105 to get 80.

$$2kx+45x=80+3k$$

Combine all terms containing x.

$$\left(2k+45\right)x=80+3k$$

The equation is in standard form.

$$\left(2k+45\right)x=3k+80$$

Divide both sides by 2k+45.

$$\frac{\left(2k+45\right)x}{2k+45}=\frac{3k+80}{2k+45}$$

Dividing by 2k+45 undoes the multiplication by 2k+45.

$$x=\frac{3k+80}{2k+45}$$