Solve 14-x/11+x=sqrt[3]{81}

$$\frac { 14 - x } { 11 + x } = \sqrt[ 3 ] { 81 }$$

Solve for x

$$x=\frac{225\times 3^{\frac{2}{3}}-75\sqrt[3]{3}-877}{82}\approx -6.30670558$$

Steps for Solving Linear Equation

Variable x cannot be equal to -11 since division by zero is not defined. Multiply both sides of the equation by x+11.

$$14-x=\left(x+11\right)\sqrt[3]{81}$$

Use the distributive property to multiply x+11 by \sqrt[3]{81}.

$$14-x=x\sqrt[3]{81}+11\sqrt[3]{81}$$

Subtract x\sqrt[3]{81} from both sides.

$$14-x-x\sqrt[3]{81}=11\sqrt[3]{81}$$

Subtract 14 from both sides.

$$-x-x\sqrt[3]{81}=11\sqrt[3]{81}-14$$

Combine all terms containing x.

$$\left(-1-\sqrt[3]{81}\right)x=11\sqrt[3]{81}-14$$

The equation is in standard form.

$$\left(-\sqrt[3]{81}-1\right)x=11\sqrt[3]{81}-14$$

Divide both sides by -1-\sqrt[3]{81}.

$$\frac{\left(-\sqrt[3]{81}-1\right)x}{-\sqrt[3]{81}-1}=\frac{33\sqrt[3]{3}-14}{-\sqrt[3]{81}-1}$$

Dividing by -1-\sqrt[3]{81} undoes the multiplication by -1-\sqrt[3]{81}.

$$x=\frac{33\sqrt[3]{3}-14}{-\sqrt[3]{81}-1}$$

Divide 33\sqrt[3]{3}-14 by -1-\sqrt[3]{81}.

$$x=-\frac{\left(33\sqrt[3]{3}-14\right)\left(9\times 3^{\frac{2}{3}}+1-3\sqrt[3]{3}\right)}{82}$$