Solve 6/8-5tx-18t/8-5t=3/4x

$$\frac{ 6 }{ 8-5t } x- \frac{ 18t }{ 8-5t } = \frac{ 3 }{ 4 } x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{24}{5}\text{, }&t\neq \frac{8}{5}\\x\in \mathrm{C}\text{, }&t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\left(5t-8\right), the least common multiple of 8-5t,4.

$$-4\times 6x+4\times 18t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply -4 and 6 to get -24.

$$-24x+4\times 18t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply 4 and 18 to get 72.

$$-24x+72t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply \frac{3}{4} and 4 to get 3.

$$-24x+72t=3x\left(5t-8\right)$$

Use the distributive property to multiply 3x by 5t-8.

$$-24x+72t=15tx-24x$$

Subtract 15tx from both sides.

$$-24x+72t-15tx=-24x$$

Add 24x to both sides.

$$-24x+72t-15tx+24x=0$$

Combine -24x and 24x to get 0.

$$72t-15tx=0$$

Subtract 72t from both sides. Anything subtracted from zero gives its negation.

$$-15tx=-72t$$

The equation is in standard form.

$$\left(-15t\right)x=-72t$$

Divide both sides by -15t.

$$\frac{\left(-15t\right)x}{-15t}=-\frac{72t}{-15t}$$

Dividing by -15t undoes the multiplication by -15t.

$$x=-\frac{72t}{-15t}$$

Divide -72t by -15t.

$$x=\frac{24}{5}$$

Solve for t

$$\left\{\begin{matrix}\\t=0\text{, }&\text{unconditionally}\\t\neq \frac{8}{5}\text{, }&x=\frac{24}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable t cannot be equal to \frac{8}{5} since division by zero is not defined. Multiply both sides of the equation by 4\left(5t-8\right), the least common multiple of 8-5t,4.

$$-4\times 6x+4\times 18t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply -4 and 6 to get -24.

$$-24x+4\times 18t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply 4 and 18 to get 72.

$$-24x+72t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply \frac{3}{4} and 4 to get 3.

$$-24x+72t=3x\left(5t-8\right)$$

Use the distributive property to multiply 3x by 5t-8.

$$-24x+72t=15xt-24x$$

Subtract 15xt from both sides.

$$-24x+72t-15xt=-24x$$

Add 24x to both sides.

$$72t-15xt=-24x+24x$$

Combine -24x and 24x to get 0.

$$72t-15xt=0$$

Combine all terms containing t.

$$\left(72-15x\right)t=0$$

Divide 0 by 72-15x.

$$t=0$$

Solve for x

$$\left\{\begin{matrix}x=\frac{24}{5}\text{, }&t\neq \frac{8}{5}\\x\in \mathrm{R}\text{, }&t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\left(5t-8\right), the least common multiple of 8-5t,4.

$$-4\times 6x+4\times 18t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply -4 and 6 to get -24.

$$-24x+4\times 18t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply 4 and 18 to get 72.

$$-24x+72t=\frac{3}{4}x\times 4\left(5t-8\right)$$

Multiply \frac{3}{4} and 4 to get 3.

$$-24x+72t=3x\left(5t-8\right)$$

Use the distributive property to multiply 3x by 5t-8.

$$-24x+72t=15tx-24x$$

Subtract 15tx from both sides.

$$-24x+72t-15tx=-24x$$

Add 24x to both sides.

$$-24x+72t-15tx+24x=0$$

Combine -24x and 24x to get 0.

$$72t-15tx=0$$

Subtract 72t from both sides. Anything subtracted from zero gives its negation.

$$-15tx=-72t$$

The equation is in standard form.

$$\left(-15t\right)x=-72t$$

Divide both sides by -15t.

$$\frac{\left(-15t\right)x}{-15t}=-\frac{72t}{-15t}$$

Dividing by -15t undoes the multiplication by -15t.

$$x=-\frac{72t}{-15t}$$

Divide -72t by -15t.

$$x=\frac{24}{5}$$