Solve 1-3x-2/5-2x+1/9=x+1/a-14x-3/15

$$1 - \frac { 3 x - 2 } { 5 } - \frac { 2 x + 1 } { 9 } = \frac { x + 1 } { a } - \frac { 14 x - 3 } { 15 }$$

Solve for a

$$a=\frac{45\left(x+1\right)}{5x+49}$$

$$x\neq -1\text{ and }x\neq -\frac{49}{5}$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 45a, the least common multiple of 5,9,a,15.

$$45a-9a\left(3x-2\right)-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

Use the distributive property to multiply 9a by 3x-2.

$$45a-\left(27xa-18a\right)-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

To find the opposite of 27xa-18a, find the opposite of each term.

$$45a-27xa+18a-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

Combine 45a and 18a to get 63a.

$$63a-27xa-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

Use the distributive property to multiply 5a by 2x+1.

$$63a-27xa-\left(10xa+5a\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

To find the opposite of 10xa+5a, find the opposite of each term.

$$63a-27xa-10xa-5a=45\left(x+1\right)-3a\left(14x-3\right)$$

Combine -27xa and -10xa to get -37xa.

$$63a-37xa-5a=45\left(x+1\right)-3a\left(14x-3\right)$$

Combine 63a and -5a to get 58a.

$$58a-37xa=45\left(x+1\right)-3a\left(14x-3\right)$$

Use the distributive property to multiply 45 by x+1.

$$58a-37xa=45x+45-3a\left(14x-3\right)$$

Use the distributive property to multiply 3a by 14x-3.

$$58a-37xa=45x+45-\left(42xa-9a\right)$$

To find the opposite of 42xa-9a, find the opposite of each term.

$$58a-37xa=45x+45-42xa+9a$$

Add 42xa to both sides.

$$58a-37xa+42xa=45x+45+9a$$

Combine -37xa and 42xa to get 5xa.

$$58a+5xa=45x+45+9a$$

Subtract 9a from both sides.

$$58a+5xa-9a=45x+45$$

Combine 58a and -9a to get 49a.

$$49a+5xa=45x+45$$

Combine all terms containing a.

$$\left(49+5x\right)a=45x+45$$

The equation is in standard form.

$$\left(5x+49\right)a=45x+45$$

Divide both sides by 5x+49.

$$\frac{\left(5x+49\right)a}{5x+49}=\frac{45x+45}{5x+49}$$

Dividing by 5x+49 undoes the multiplication by 5x+49.

$$a=\frac{45x+45}{5x+49}$$

Divide 45+45x by 5x+49.

$$a=\frac{45\left(x+1\right)}{5x+49}$$

Variable a cannot be equal to 0.

$$a=\frac{45\left(x+1\right)}{5x+49}\text{, }a\neq 0$$

Solve for x

$$x=-\frac{49a-45}{5\left(a-9\right)}$$

$$a\neq 9\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 45a, the least common multiple of 5,9,a,15.

$$45a-9a\left(3x-2\right)-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

Use the distributive property to multiply 9a by 3x-2.

$$45a-\left(27ax-18a\right)-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

To find the opposite of 27ax-18a, find the opposite of each term.

$$45a-27ax+18a-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

Combine 45a and 18a to get 63a.

$$63a-27ax-5a\left(2x+1\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

Use the distributive property to multiply 5a by 2x+1.

$$63a-27ax-\left(10ax+5a\right)=45\left(x+1\right)-3a\left(14x-3\right)$$

To find the opposite of 10ax+5a, find the opposite of each term.

$$63a-27ax-10ax-5a=45\left(x+1\right)-3a\left(14x-3\right)$$

Combine -27ax and -10ax to get -37ax.

$$63a-37ax-5a=45\left(x+1\right)-3a\left(14x-3\right)$$

Combine 63a and -5a to get 58a.

$$58a-37ax=45\left(x+1\right)-3a\left(14x-3\right)$$

Use the distributive property to multiply 45 by x+1.

$$58a-37ax=45x+45-3a\left(14x-3\right)$$

Use the distributive property to multiply 3a by 14x-3.

$$58a-37ax=45x+45-\left(42ax-9a\right)$$

To find the opposite of 42ax-9a, find the opposite of each term.

$$58a-37ax=45x+45-42ax+9a$$

Subtract 45x from both sides.

$$58a-37ax-45x=45-42ax+9a$$

Add 42ax to both sides.

$$58a-37ax-45x+42ax=45+9a$$

Combine -37ax and 42ax to get 5ax.

$$58a+5ax-45x=45+9a$$

Subtract 58a from both sides.

$$5ax-45x=45+9a-58a$$

Combine 9a and -58a to get -49a.

$$5ax-45x=45-49a$$

Combine all terms containing x.

$$\left(5a-45\right)x=45-49a$$

Divide both sides by -45+5a.

$$\frac{\left(5a-45\right)x}{5a-45}=\frac{45-49a}{5a-45}$$

Dividing by -45+5a undoes the multiplication by -45+5a.

$$x=\frac{45-49a}{5a-45}$$

Divide 45-49a by -45+5a.

$$x=\frac{45-49a}{5\left(a-9\right)}$$