Solve 10x-3/3+5x+2/4+3z=5

$$\frac { 10 x - 3 } { 3 } + \frac { 5 x + 2 } { 4 + 3 z } = 5$$

Solve for x

$$x=\frac{6\left(9z+11\right)}{5\left(6z+11\right)}$$

$$z\neq -\frac{11}{6}\text{ and }z\neq -\frac{4}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(3z+4\right), the least common multiple of 3,4+3z.

$$\left(3z+4\right)\left(10x-3\right)+3\left(5x+2\right)=15\left(3z+4\right)$$

Use the distributive property to multiply 3z+4 by 10x-3.

$$30zx-9z+40x-12+3\left(5x+2\right)=15\left(3z+4\right)$$

Use the distributive property to multiply 3 by 5x+2.

$$30zx-9z+40x-12+15x+6=15\left(3z+4\right)$$

Combine 40x and 15x to get 55x.

$$30zx-9z+55x-12+6=15\left(3z+4\right)$$

Add -12 and 6 to get -6.

$$30zx-9z+55x-6=15\left(3z+4\right)$$

Use the distributive property to multiply 15 by 3z+4.

$$30zx-9z+55x-6=45z+60$$

Add 9z to both sides.

$$30zx+55x-6=45z+60+9z$$

Combine 45z and 9z to get 54z.

$$30zx+55x-6=54z+60$$

Add 6 to both sides.

$$30zx+55x=54z+60+6$$

Add 60 and 6 to get 66.

$$30zx+55x=54z+66$$

Combine all terms containing x.

$$\left(30z+55\right)x=54z+66$$

Divide both sides by 30z+55.

$$\frac{\left(30z+55\right)x}{30z+55}=\frac{54z+66}{30z+55}$$

Dividing by 30z+55 undoes the multiplication by 30z+55.

$$x=\frac{54z+66}{30z+55}$$

Divide 54z+66 by 30z+55.

$$x=\frac{6\left(9z+11\right)}{5\left(6z+11\right)}$$

Solve for z

$$z=-\frac{11\left(5x-6\right)}{6\left(5x-9\right)}$$

$$x\neq -\frac{2}{5}\text{ and }x\neq \frac{9}{5}$$

Steps for Solving Linear Equation

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

$$\left(3z+4\right)\left(10x-3\right)+3\left(5x+2\right)=15\left(3z+4\right)$$

Use the distributive property to multiply 3z+4 by 10x-3.

$$30zx-9z+40x-12+3\left(5x+2\right)=15\left(3z+4\right)$$

Use the distributive property to multiply 3 by 5x+2.

$$30zx-9z+40x-12+15x+6=15\left(3z+4\right)$$

Combine 40x and 15x to get 55x.

$$30zx-9z+55x-12+6=15\left(3z+4\right)$$

Add -12 and 6 to get -6.

$$30zx-9z+55x-6=15\left(3z+4\right)$$

Use the distributive property to multiply 15 by 3z+4.

$$30zx-9z+55x-6=45z+60$$

Subtract 45z from both sides.

$$30zx-9z+55x-6-45z=60$$

Combine -9z and -45z to get -54z.

$$30zx-54z+55x-6=60$$

Subtract 55x from both sides.

$$30zx-54z-6=60-55x$$

Add 6 to both sides.

$$30zx-54z=60-55x+6$$

Add 60 and 6 to get 66.

$$30zx-54z=66-55x$$

Combine all terms containing z.

$$\left(30x-54\right)z=66-55x$$

Divide both sides by 30x-54.

$$\frac{\left(30x-54\right)z}{30x-54}=\frac{66-55x}{30x-54}$$

Dividing by 30x-54 undoes the multiplication by 30x-54.

$$z=\frac{66-55x}{30x-54}$$

Divide 66-55x by 30x-54.

$$z=\frac{11\left(6-5x\right)}{6\left(5x-9\right)}$$

Variable z cannot be equal to -\frac{4}{3}.

$$z=\frac{11\left(6-5x\right)}{6\left(5x-9\right)}\text{, }z\neq -\frac{4}{3}$$