Solve frac{sqrt{72}}{6}*(x+16/10)=sqrt{2}*(11/5+2x)

$$\frac { \sqrt { 72 } } { 6 } \cdot ( x + \frac { 16 } { 10 } ) = \sqrt { 2 } \cdot ( \frac { 11 } { 5 } + 2 x )$$

Solve for x

$$x=-\frac{3}{5}=-0.6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 6,10,5.

$$5\sqrt{72}\left(x+\frac{16}{10}\right)=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$5\times 6\sqrt{2}\left(x+\frac{16}{10}\right)=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Multiply 5 and 6 to get 30.

$$30\sqrt{2}\left(x+\frac{16}{10}\right)=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$30\sqrt{2}\left(x+\frac{8}{5}\right)=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Use the distributive property to multiply 30\sqrt{2} by x+\frac{8}{5}.

$$30\sqrt{2}x+30\sqrt{2}\times \frac{8}{5}=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Express 30\times \frac{8}{5} as a single fraction.

$$30\sqrt{2}x+\frac{30\times 8}{5}\sqrt{2}=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Multiply 30 and 8 to get 240.

$$30\sqrt{2}x+\frac{240}{5}\sqrt{2}=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Divide 240 by 5 to get 48.

$$30\sqrt{2}x+48\sqrt{2}=30\sqrt{2}\left(\frac{11}{5}+2x\right)$$

Use the distributive property to multiply 30\sqrt{2} by \frac{11}{5}+2x.

$$30\sqrt{2}x+48\sqrt{2}=30\sqrt{2}\times \frac{11}{5}+60x\sqrt{2}$$

Express 30\times \frac{11}{5} as a single fraction.

$$30\sqrt{2}x+48\sqrt{2}=\frac{30\times 11}{5}\sqrt{2}+60x\sqrt{2}$$

Multiply 30 and 11 to get 330.

$$30\sqrt{2}x+48\sqrt{2}=\frac{330}{5}\sqrt{2}+60x\sqrt{2}$$

Divide 330 by 5 to get 66.

$$30\sqrt{2}x+48\sqrt{2}=66\sqrt{2}+60x\sqrt{2}$$

Subtract 60x\sqrt{2} from both sides.

$$30\sqrt{2}x+48\sqrt{2}-60x\sqrt{2}=66\sqrt{2}$$

Combine 30\sqrt{2}x and -60x\sqrt{2} to get -30\sqrt{2}x.

$$-30\sqrt{2}x+48\sqrt{2}=66\sqrt{2}$$

Subtract 48\sqrt{2} from both sides.

$$-30\sqrt{2}x=66\sqrt{2}-48\sqrt{2}$$

Combine 66\sqrt{2} and -48\sqrt{2} to get 18\sqrt{2}.

$$-30\sqrt{2}x=18\sqrt{2}$$

The equation is in standard form.

$$\left(-30\sqrt{2}\right)x=18\sqrt{2}$$

Divide both sides by -30\sqrt{2}.

$$\frac{\left(-30\sqrt{2}\right)x}{-30\sqrt{2}}=\frac{18\sqrt{2}}{-30\sqrt{2}}$$

Dividing by -30\sqrt{2} undoes the multiplication by -30\sqrt{2}.

$$x=\frac{18\sqrt{2}}{-30\sqrt{2}}$$

Divide 18\sqrt{2} by -30\sqrt{2}.

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