Solve 10/a-50/3x=31/3

$$\frac { 10 } { a } - \frac { 50 } { 3 x } = 3 \frac { 1 } { 3 }$$

Solve for a

$$a=\frac{3x}{x+5}$$

$$x\neq 0\text{ and }x\neq -5$$

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 3ax, the least common multiple of a,3x,3.

$$3x\times 10-a\times 50=ax\left(3\times 3+1\right)$$

Multiply 3 and 10 to get 30.

$$30x-a\times 50=ax\left(3\times 3+1\right)$$

Multiply 3 and 3 to get 9.

$$30x-a\times 50=ax\left(9+1\right)$$

Add 9 and 1 to get 10.

$$30x-a\times 50=ax\times 10$$

Subtract ax\times 10 from both sides.

$$30x-a\times 50-ax\times 10=0$$

Multiply -1 and 50 to get -50.

$$30x-50a-ax\times 10=0$$

Multiply -1 and 10 to get -10.

$$30x-50a-10ax=0$$

Subtract 30x from both sides. Anything subtracted from zero gives its negation.

$$-50a-10ax=-30x$$

Combine all terms containing a.

$$\left(-50-10x\right)a=-30x$$

The equation is in standard form.

$$\left(-10x-50\right)a=-30x$$

Divide both sides by -50-10x.

$$\frac{\left(-10x-50\right)a}{-10x-50}=-\frac{30x}{-10x-50}$$

Dividing by -50-10x undoes the multiplication by -50-10x.

$$a=-\frac{30x}{-10x-50}$$

Divide -30x by -50-10x.

$$a=\frac{3x}{x+5}$$

Variable a cannot be equal to 0.

$$a=\frac{3x}{x+5}\text{, }a\neq 0$$

Solve for x

$$x=-\frac{5a}{a-3}$$

$$a\neq 0\text{ and }a\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3ax, the least common multiple of a,3x,3.

$$3x\times 10-a\times 50=ax\left(3\times 3+1\right)$$

Multiply 3 and 10 to get 30.

$$30x-a\times 50=ax\left(3\times 3+1\right)$$

Multiply 3 and 3 to get 9.

$$30x-a\times 50=ax\left(9+1\right)$$

Add 9 and 1 to get 10.

$$30x-a\times 50=ax\times 10$$

Subtract ax\times 10 from both sides.

$$30x-a\times 50-ax\times 10=0$$

Multiply -1 and 50 to get -50.

$$30x-50a-ax\times 10=0$$

Multiply -1 and 10 to get -10.

$$30x-50a-10ax=0$$

Add 50a to both sides. Anything plus zero gives itself.

$$30x-10ax=50a$$

Combine all terms containing x.

$$\left(30-10a\right)x=50a$$

Divide both sides by 30-10a.

$$\frac{\left(30-10a\right)x}{30-10a}=\frac{50a}{30-10a}$$

Dividing by 30-10a undoes the multiplication by 30-10a.

$$x=\frac{50a}{30-10a}$$

Divide 50a by 30-10a.

$$x=\frac{5a}{3-a}$$

Variable x cannot be equal to 0.

$$x=\frac{5a}{3-a}\text{, }x\neq 0$$