Solve 2x+sqrt{16}=8frac{sqrt{24}}{3}

$$2 x + \sqrt { 16 } = 8 \frac { \sqrt { 24 } } { 3 }$$

Solve for x

$$x=\frac{8\sqrt{6}}{3}-2\approx 4.531972647$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$6x+3\sqrt{16}=8\sqrt{24}$$

Calculate the square root of 16 and get 4.

$$6x+3\times 4=8\sqrt{24}$$

Multiply 3 and 4 to get 12.

$$6x+12=8\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$6x+12=8\times 2\sqrt{6}$$

Multiply 8 and 2 to get 16.

$$6x+12=16\sqrt{6}$$

Subtract 12 from both sides.

$$6x=16\sqrt{6}-12$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{16\sqrt{6}-12}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{16\sqrt{6}-12}{6}$$

Divide 16\sqrt{6}-12 by 6.

$$x=\frac{8\sqrt{6}}{3}-2$$